Anki is an open-source flashcard app for Windows, Linux, Mac OSX with versions also available for Android and iOS. Unfortunately, iOS version costs $25, but all other versions are free.
Anki is a self-graded flashcard program / app. This makes it a combination quiz-app + timer system. Unlike Duolingo or other programs, Anki entirely relies upon self-grading, but this is more than sufficient for study.
Anki grabs the top cards from a deck (defaulting to 20 new cards per day. Feel free to customize this to whatever fits your needs best). Then each day, it grabs "scheduled review" cards + shuffles in the new cards, and shows you them one at a time. Once a card is shown to you, you the user click a button to reveal the other side.
After the flip, Anki asks you to self-grade yourself on your performance. "Again" means you grade yourself as "incorrect", and Anki will remember this mistake. Because you were "incorrect" on this card, Anki will show you the card again very soon.
If you choose one of the three "correct" scores (labeled "Hard", "Good" and "Easy"), Anki remembers that you've answered correctly, and will schedule the card some time in the future. I'll get to the difference of the three scores later, but consider all three to just be "correct" for now.
The precise time is calculated based on how well Anki thinks you know the card. If you know the card well, "Good" might schedule the card to be reviewed 1 month from now, but if you've made a lot of mistakes with a particular card, then that card will likely be reviewed 1 or 2 days from now. Its all data collected on a per-card basis.
Above is an example screenshot of Anki's memory: every single self-graded score is remembered on every single card, as well as the date and time of each score.
As such, Anki is a system of spaced repetition. The "better" you are with some cards, the less you see them. The "worse" you are with other cards, the more Anki shows you those particular cards you keep making mistakes with. Timer + self-grading == you only see the cards you're doing bad with, while Anki hides the cards you are doing good with.
The Algorithm
FSRS is a new experimental algorithm Anki is using. There's been 6 versions (FSRS-1, -2, -3,... and of course FSRS 6 today). Fortunately, the overall gist has been the same for all 6 versions. Alas, its a lot of blogposts and technical math that's far too nerdy for most people https://github.com/open-spaced-repetition/fsrs4anki/wiki/The-Algorithm. For the math nerds who want to learn the algorithm, study away. But I'll attempt to do a simpler "translation".
Before we get started, click on your deck's preferences and scroll down to the FSRS button. Ensure it is on.
FSRS is simply three pieces of memory being applied to each and every "card" in your Anki decks. Every single card will try to figure out "R", "S" and "D". R is the probability that you've forgotten a card each day. The longer a card goes without being shown, the worse-and-worse "R" gets (this is the value Anki uses to determine when to repeat a card to you, it wants to show you a card before you've forgotten, but after enough time that you had a chance to forget, defaulting to 10% chance of forgetting).
Every single card tracked by Anki has this "forgetting" curve, primarily defined by the "R" aka Retention variable.
The theory is: if you show a card too often, you never really test your long-term memory. Furthermore, its too much extra work to review so many cards. By waiting days, weeks, or months before showing you a card again, Anki saves you time by not overly-reviewing cards you already know the information of. Furthermore, studies have shown that showing you information "right as you are forgetting about it" is the best way to remember (!!!). Any sooner, and you really aren't learning too well, but instead just temporarily holding things in your short-term or medium-term memory.
"S" stands for Stability. The more "stable" a card is, the longer Anki-FSRS thinks it can stay in your memory memory without review. Most "new" cards are assumed to be forgotten about within a day by default. However, as you get the card "correct" over-and-over again, Anki-FSRS will increase stability, thereby causing the longer review intervals. (Maybe showing you a card once every 3 days, then 7 days, then 1.5 months, then 3 months....).
"D" stands for Difficulty. The more times you get a card wrong (ie: when you click the "Again" button), the worse Difficulty gets. Anki-FSRS remembers that some cards are harder for you to remember... in particular the ones you keep getting wrong.
Even if you get a high-difficulty card correct multiple times, Anki "remembers" that you have been forgetting this card, and will show it to you again sooner. Ex: by default Anki will mature a card within 7x correct answers in a row. However, if a card is "difficult", Anki will keep showing you that card 10x, 15x or more, knowing that you need the extra practice.
Or in more math-nerd terms, "Difficulty" is the derivative of stability. The change-of-stability is determined by the "Difficulty" of a card.
Hard / Good / Easy
Hard / Good / Easy all count as correct (ie: increases the stability of Anki-FSRS), but will do different things to your Difficulty score.
"Good" is the default, and Anki recommends that users hit the "Good" button 80%+ of the time. Lets pretend that a particular "Good" answer will result in 1-month timer for a particular card...
"Easy" basically is telling Anki that you don't want to practice with this card anymore (ie: low-difficulty card). After clicking "Easy", instead of taking a 1-month timer... Anki will likely choose a 1.5-month or 2-month timer on the card.
"Hard" is telling Anki that you want extra practice with this card. It increases difficulty, despite increasing stability. You'll see this card again more-and-more in the future. Instead of 1-month timer, Anki might show you the card again within 2-weeks.
Where Anki fits in language learning
Anki was originally developed to help its original programmer learn Japanese. Its not an end-all be-all app however. Anki is only a piece of any language-learner. You must also buy grammar / theory books, as well as write regularly in the new language... speaking and listening and more.
Nonetheless, "Anki" is your cudgel. A brute-force method to try to force vocabulary words into your brain through raw force. You'll likely never gain mastery of the words through Anki... but you can at least become a beginner and learn how to start reading. There's literally thousands, if not tens-of-thousands of words you must learn to become proficient in a language. And that's spelling, grammar usage (gender / der/das/die in German, or maybe conjugation rules and pluralization rules), definitions and more!!
In all cases, Anki can be used as a way to force this information into your brain, getting it ready so that those words can "begin to be learned" when you watch TV, listen to a foreign language podcast or hear those words in a song.
Yes, Anki isn't enough. But Anki is a great tool to get you started. And getting started is sometimes the hardest step for many people.
Remember: 1000 words is beginner level (near 1st grade level understanding), while 10,000 words is roughly high school level. If you wish to be seen as a competent adult in a new language, you must figure out a system to reach those 10,000+ words known. 10,000 words sounds like a lot in isolation... especially because true mastery of 10,000 words includes spelling, grammar (pluralization/conjugation/gender), meaning, and pronunciation. But think about it: 10,000 words is merely 14 words per day for 2-years. Plenty of people have used Anki to jumpstart that kind of long-term forced-learning of words.
My Anki routine
My current Anki deck is the 4000 German words/phrases by frequency (https://ankiweb.net/shared/info/653061995). Anki decks vary in quality but this is one of the better German decks.
Despite that, this deck starts out-of-order. I had to reorder the first 200 words into the correct order (for some reason, words #1 through #200 were actually the least frequent words). After reordering, I hit the "FSRS" button, signed up to AnkiWeb.com and synchronized my Desktop + Phone to this deck through the web-account.
I currently keep the defaults of Anki-FSRS at 90% retention and 20 words per day. I roughly have 80 review words per day + 20 new words, or 100 flashcards to review (front and back). I hit "good" or "again" most often, though some very easy words (ex: "Ich") I do hit the "easy" button on. I rarely hit "hard" at all.
When a card feels poorly made, I always go into "Edit" and improve the card. In most cases, the "English side" of this deck is lacking (ex: "because" either turns into weil or denn). In these cases, I add a German sentence to the English side with the German-word missing, so that the card can become "more fair" as study material. Anki Decks should always be customized to become your own notes.
If Anki gives me a new word, I also check Wiktionary for the proper pronounciation, as well as additional "example sentences" of that word. Anki is NOT a dictionary, its simply a notecard system, and you should rely upon good and proper dictionaries. In some rare cases, I go to German Language Discord and ask the community to help me understand a concept, but in most cases I do try to figure out the word myself.
I also use many songs, kids songs, Anime songs, pop songs and more as my primary source of "Practical German". (Ideally songs harder than Ramstein's "Du Hast", lol). I'm building an Anki deck out of these songs (ex: Backe Backe Kuchen, or "Bake Bake a Cake", a traditional German kid's song, has a list of common ingredients like sugar, salt, milk. Its good vocabulary practice... and also is a good source of practical words for an Anki deck). I also have a beginner German book ("Cafe in Berlin"), with a huge vocabulary list. Fortunately, the author for this book already made an Anki deck and I can just go to to the listed website and download the pre-made Anki.
Oh, one more thing. There are also "Grammar Workbooks" which consist of hundreds of pages worth of drills.
If you are a nerd, these hundreds of pages of exercises might be more important than reference material. Buying a workbook so that you can DIRECTLY write on the pages and try immediately is also helpful.
Grammatik Aktiv by Cornelsen covers A1 through B1 pencil-and-paper drills. Very dry stuff but it kind of works...
You need a separate textbook to know what order to learn things (it sounds like your Goethe Institute course covers this). You need additional reference (Basic German: A Grammar and Workbook covers this, a 2nd clear perspective focusing on grammar). Finally you'll find that various bits of your speaking + writing skills suck.
Using Grammatik Aktiv exercises to drill on your weaknesses just makes sense. Maybe an intensive would try to complete the whole book but uhhhhh.... self study means you get to choose when you're done with exercises lol. Do as much as you see fit.
Grammatik Aktiv is however, 100% in German. You probably need to wait until you are A1+ before you buy Grammatik Aktiv, if only so you have enough vocabulary to even figure out what the drills are asking of you.
Maybe your A1 goal should be to learn enough German so that you can start Grammatik Aktiv, lol.