Depending on the size of the burn, pinch or cut off a tip of a "leaf" and put the juice - it's more gel-like though - on the burn. You can also just split it open and lay the whole thing on there. Maybe wrap it with some gauze around it for a little bit if you want or don't have time to just "sit there" a while.
It'll burn like a bitch when you put it on - "drawing out the fire" is how southerners put it, but no blister no nothing when it's all said and done. Put it on and forget about it. It'll dry. If it still "hurts" after it's dry, you might want to put on a little more again. Don't put it in your mouth, though, that stuff is bitter as hell.
I've lots of smaller burn stories - I splashed hot grease on my hand. Coated my hand, but missed one tiny spot between my fourth and pinky finger. Nada where the aloe went. Honking blister on the spot I missed. Etc . . .
Two larger stories - my brother was working on his motorcycle. Accidentally lay his left forearm against the tailpipe. Mom used up nearly every plant in the house but - no blisters or anything.
Fifteen years later my dad - who had something of a green thumb - had grown some of the biggest damn aloe plants I've ever seen. They were like two feet across - very large long leaves. Anyway, my mother was cooking and spilled either boiling water or hot grease (I don't remember which now - that was a about twenty years ago) - dad went out, cut off a whole leaf. Split it open and wrapped it to her arm. Et voila, good as new.
It truly does work that way. This story has not been exaggerated in any way. Keep it on the windowsill in the kitchen. Don't overwater. The leaves will let you know when it needs watering because they won't be as "plump".
Of course, I kill every plant I've ever bought, so I don't have one. (Then again, I don't do much cooking anymore, either.)
The gel is sold OTC now, but I have no idea if that is as efficacious as straight from the source.