Garlic and onions first, mushrooms next (salt them so they release their liquids and brown), carrots/sweet potato/potato/beets/ any other very dense veggies next, then broccoli/Brussels sprouts and cauliflower types of brassicas, then cabbage/kale/chard, then lighter leafy greens. With things like spinach and arugula I pretty much turn off the heat and fold them in whatever I'm making immediately and toss and they'll cook down. It is also debated whether garlic should be added early or not, you can kinda do with it what you will.

A lot of this comes down to trial and error in terms of how long to cook things before adding the next. Use a fork to poke, and use your teeth to bite. Say if I'm cooking broccoli, I'll give it 5 minutes then eat a small piece to see if I like the texture. Hard as a rock still? Another few minutes, poke with a fork, if its softer but still tough, ill add the next "layer" of veg. If I'm just adding leafy greens I'll let things like sweet potato/carrot/brocc cook all the way through then add those and cook for 1-2 minutes.