By "hands free" I'm mainly referring to orgasming without touching the penile shaft, but rather stimulating some other sensitive body part¹.

Let's start from the absolute basics: there are a variety of different kinds of orgasm which require different kinds/amounts of stimulation to achieve, can feel pretty substantially different, and are more or less tightly coupled to ejaculation. On top of that, HRT will also significantly change a lot of variables here. I'll try and go through one step at a time and explain first how it works in a testosterone-dominant body (or rather: how it worked for me), and then how it changes on E. There's probably a lot of stuff I'm skipping over here; I'm only discussing stuff I've experimented with myself or have heard in discussions with multiple other people. Also, keep in mind that most of the stuff here can vary a TON from person to person - heck, some cis women can't do multiple orgasms! This is intended as a kicking-off point for you to do more research on your own.

The penile orgasm is the most basic one, and is probably the only one that 90% of straight guys will ever have. On T, triggering it is extremely easy - literally just rub up-and-down along the shaft and/or tip of the penis, and just absolutely go to town using the medium of your choice: vagina, mouth, hand, fleshlight, rubber glove in a pringles can, whatever. The resulting orgasm is short and extremely intense, with most of the pleasurable sensation being concentrated in and near the penis itself, and is nearly inseparable from ejaculation. Once ejaculation has occurred, there's generally a fairly long refractory period before another one is possible, and each subsequent round is more difficult to achieve and less intense.
The most other most widely known kind of orgasm for bodies on T is the prostate orgasm, which is triggered by stimulating the prostate either through pressing around the taint, or reaching it more directly via the anus (ideally using a dedicated prostate massager). If done correctly, prostate orgasms won't result in a full erection or ejaculation², and are immensely pleasurable in exactly the opposite way of a "conventional" orgasm. It takes a fair amount of patience and being in the right headspace to actually notice anything, and the sensation is relatively subtle so for someone used to penile orgasms it'll be hard to notice anything going on. The best way I can describe it is a continuous series of 5-10 second "waves" of pleasure which aren't particularly intense (but still quite fun!), and the sensation is more spread across the entire lower body.
For lack of better terminology, I'm going to refer to this next one as a "girl orgasm", by which I'm referring to the stereotypical female orgasm: long, intense (less than a penile orgasm, though), the pleasurable sensations seems to originate in the brain and spread from there to the whole body, and little to no refractory period. For me, this was always the "holy grail" of the sexual experience, and with a lot of practice (and many failed attempts along the way), it is possible for someone on T to achieve these. Ideally, it'd also cause little to no erection, and no ejaculation. There are a number of different techniques floating around for how to pull this off, from carefully controlled edging to clamping down the pelvic floor muscles as hard as possible immediately before ejaculating. The only thing I found that seemed to work is by completely relaxing EVERY muscle, and then make tiny movements using just the tip of a finger to stimulate only the penile frenulum (CW: images of genetalia). If your pelvic floor muscles flex at all (the muscles around the base of the penis which flex during regular penile stimulation and pulse during ejaculation), or if your penis get more than like half-erect, that means you're stimulating too much and switched over to regular penile orgasm mode - stop for a while and start back from the beginning! With a lot of practice you'll eventually get to the point that you can feel a very different sort of pleasure in your mind (not in your penis!) and if you're in exactly the right mental state you can eventually push far enough to get a full-on girl orgasm - and with even more practice you can eventually pull this off multiple times in a row. Huge amount of work, takes weeks/months of practice, and isn't more than like 50% reliable even under ideal circumstances.

Okay, now we can move on to what changes post-HRT! First off, the conventional penile orgasm gets harder to achieve and less pleasurable. For a few tgirls I've spoken to, the same kind of up-and-down stimulation of the penile shaft now actually causes them to have a proper girl orgasm, but for most people it seems like that kind of stimulation simply becomes a lot less effective or becomes actively uncomfortable, and if you do orgasm in that way, it simply won't feel as intense as it used to pre-transition. Ejaculation will probably happen; the ejaculate is now clear due to lack of sperm.
At least in my experience, prostate orgasms still work the same. More research may be necessary. wink wink
The real game changer is that girl orgasms are much easier to achieve reliably! The entire buildup process becomes much more forgiving - you can actually twitch your hips or roll your head back or clench your pelvic floor or ... without having to reset back to zero, you can let your mind drift without all the sexual "pressure" being transferred to the penis and being converted to an ordinary penile orgasm, you don't have to be extremely precise with where and how you stimulate. Most/all of the new erogenous zones estrogen unlocks (boobs, tummy, hips, ass, inner thighs, neck, ...) seem to build up towards this sort of orgasm. For some transfems, stimulating the penis in certain ways (most notably: using a vibrator on the head) apparently triggers girl orgasms post-HRT. Personally, I can't reproduce this; any kind of penile stimulation triggers a (somewhat underwhelming) penile orgasm. Maybe I've just got to wait longer for HRT to work its magic?

Finally, I'll add that learning how to recognize which body parts to stimulate in which way, and more importantly how different kinds of arousal and orgasm feel (especially in the early buildup stages) will probably require a fair amount of solo practice :)

¹ It's definitely possible to orgasm and/or ejaculate without any physical stimulation at all, but that requires you to be exceptionally horny - I've only ever managed to pull that off during very elaborate self-bondage sessions.
² There might be get some (or a lot or) precum, though :P