Lots of stuff in the archives for it if you do a search for "unconditional parenting" or "alfie kohn" :)
I'm always linking this on here but my friend's website (just a collection of thoughts really, nothing fancy, nothing for sale) has got a section on gentle discipline (UP principles included) and she seems to have covered almost every angle really succinctly. Link here.
I think the thing about UP is it isn't a discipline technique in itself, it's a set of principles by which the author believes discipline should be conducted. There are lots of techniques which fit in with the UP philosophy, they just take more finding and creative thinking. A formulaic "system" isn't going to work with it.
But yes, on to your questions. DS is 2 next week, if that's relevant.
Tantrums: If I haven't managed to head it off and he doesn't want holding then I let him ride it out and carry on with what I was doing. So not ignoring specifically, but not mithering him either, and making myself available so that when he has finished he can come up for a hug and/or a chat if he wants to.
Praise: I try to follow his lead. If he seems pleased with himself I join in and say "Wow, that is a big tower!" or whatever, but I don't say "Well done!" every time he puts in a jigsaw piece correctly. I read this somewhere and it made sense to me. If he does something like helps me tidy up I say "thank you DS, that's really helpful," rather than "good boy" (although I do slip into good boy etc as well). Encouragement, I suppose he's a bit young yet, but occasionally he will say something like "Doesn't work" with a jigsaw piece which he's got nearly right and I'll say "Try again, how about this way, let's turn it round" etc. He knows the word for help and will ask for it if he wants it.
Unruliness in social situations - depends what it is. If he is not bothering anyone else - e.g. the other night we went out for dinner at a pub and he kept putting his foot (no shoes) on the table. I tried moving it off but he wouldn't keep it down so we ignored it in the end. When he is older he can understand that certain places have different rules and if you want to go to these places you need to abide by them.
If bothering other people then it is the same as any other dangerous or destructive behaviour. Distraction, reasoning, explanation, depending on ages. Explanation beforehand of the way they are expected to behave in the situation, and prior planning as well. Think about whether something is expecting too much from a child of that age and whether there is a compromise situation, e.g. spending the morning outdoors if the afternoon is going to be sitting still. Last resort is removal from the situation entirely. Sometimes things are necessary - leaving would not be a punishment; though the child might be upset by it, they also might not. There is no need to impose a further "sanction" either way, which is where the difference lies. TBH I think this is Kohn's weakest point. Sometimes it is necessary to do something which might upset your child, just like you might upset a friend by being honest with them about something. You can do it respectfully - give warnings, explain why, and validate feelings "I know it's disappointing when you have to stop what you are doing."
School etc - have not come across school yet, so not sure. Other caregivers I have had a degree of choice and been able to choose a childminder who is similar in approach, and I think DS will probably go to the local Montessori pre-school so that is similar too. The biggest difference is when DS goes to his Dad's (we are not together) and I'm not sure what his approach is but I suspect it's very different from mine. If I have learned one thing from this and various talks I've had etc it's that children are very adaptable and learn very quickly to switch between one set of rules and another, especially if you stay consistent with yourself. You are his main caregiver, so yours will be the defining factor, I would have thought. I tend (or I try!) not to worry about it too much.
Haven't had criticism yet(!) touch wood! Only on online forums etc, where I can always write out a long reply. Usually I find people object on some ridiculous level like "Oh, UP means not disciplining at all!" which isn't true, so I just try to explain how it does work. It is difficult to explain though, especially in one sentence. The main difficulty is that most discipline strategies can be explained in one sentence. E.g. "When he acts up he goes on the naughty step for three minutes" or "When he is good he gets a sticker. When he gets ten stickers he gets a prize." whereas this isn't easy to explain like that because each situation is dealt with as it comes up. It's not one size fits all. (But that's what I like about it!)
Sorry this is so long, my posts on this subject always are!