In this wonderful internet age there are plenty of videos and step by step instructions for setting up instruments. The good news about a uke is that there are fewer adjustments available than on some other types of stringed instruments (a modern electric guitar, for example) which makes them easier to set up in the sense of fewer variables to worry about and less interaction between variables. The bad news is, this also means it's harder to set one up, in some cases at least, in the sense that some problems are difficult or impossible to fully solve on some instruments for some player's preferences.
I think it's worth pointing out, too, that it's totally fine to "just play" and not get too concerned with your setup unless or until you notice a specific problem. As merlin pointed out, if it ain't broke, don't fix it. It can be very educational to teach yourself how to set up a uke, but you may very well find that - after learning all the steps - you sit down with one of your instruments, run through it, and don't end up actually making any adjustments! You may also find that you literally can't tell a difference between two different action heights, and rather than interpreting that as an issue or a problem to solve, that may well mean that the difference literally doesn't make a difference for you, and that's okay too.
Essentially, when thinking about a setup, there's a foundation you need to start from. An instrument that is intact, without damage, and was well designed. This includes some of the non-adjustable or hard-to-adjust things on a uke which need to be more or less correct - bridge is in the correct position for the scale length, frets are intact (not loose) and level, and the neck has an appropriate amount of relief built in (since ukes don't usually have adjustable truss rods). The majority of quality instruments will have those things well addressed, but if you're buying a questionable instrument, or a used instrument with an unknown history, it can be helpful to know how to check them.
Assuming the foundation is good, you really have three potential adjustments. I like to think of them all as feedback loops, rather than things you can specify ahead of time (at least when approach setups in the generic sense, versus for a specific known instrument):
1) Setting up the nut. Think of the nut as the "zero fret." It stops the string in the open position, in the same way that the 12th fret stops it at the 12th position. The nut needs to be a good fit to the neck and the end of the fretboard. Nuts are sometimes glued in place, which needs to be done cautiously (with a small amount of weak glue) such that the nut is still removable. Glue residue needs to be cleaned out any time a nut is removed, otherwise it can mean that the nut doesn't sit right. The slots in the nut need to be appropriately sized for the string gauges you're using - the string should sit down in the slot, and needs to be loose enough that it can easily slide over the nut as you tune, but not so loose that it's not precisely located. Slots are typically anywhere from half to 2/3rds the depth of the string - they don't need to come up higher than that, although it's really just for aesthetics. Checking all those things should probably count as "foundational" in my above paragraph, but nuts are often replaced during a setup so I suppose that's debatable. The one variable you do often see specified as part of a setup is the nut height. Many people have different ways of determining the nut height, but ultimately it's a matter of preference. The nut needs to be high enough to not cause open strings to buzz on the first fret, but low enough that it doesn't require undue pressure to fret notes on the lower frets - which is a matter of playability, but also a matter of keeping the instrument in tune with itself, since really high nut heights can cause intonation issues. The method I use to set nut height is to determine the acceptable gap between the string and the second fret when that string is fretted at the first fret, then set the nut such that the string has that much clearance over the first fret when not fretted. That's a bit of a run-on sentence, but it goes back to considering the nut as the zero fret - when you fret a given fret, the string needs a certain clearance over the next-highest fret in order to not buzz. So, when you "fret the zero fret" (play the string in open position, not actually fretted) you need that same clearance over the first fret. I find this method creates a very consistent feel and a very consistent playability between the frets and the open strings. To be clear, I don't have a default spec in mind and I don't aim for a specific value, I measure and set each instrument accordingly.
2) Setting the saddle height. The saddle height determines the action - the distance between the strings and the frets, i.e. the 2.5mm or 3mm at the 12th fret you're quoting for your setups. Action, of course, determines how much room the string has to vibrate before it will buzz on a fret. It also determines the ease of fretting a note, since higher action means you'll feel that it's harder to get the string pressed down. Action is also indirectly influenced by relief - and this is one of the stumbling blocks for setting up a uke, since relief is often not adjustable. An instrument with too much or too little relief will need a different string height to arrive at the same effective clearance for a vibrating string. Strings of different length (i.e. a tenor compared to a soprano) will need different clearance, too. So while it can be useful to know "I like the feel of 3mm on this uke" that doesn't, by default, mean that you will always like 3mm on all ukes. Knowing an action you like on a specific scale length with a specific brand/gauge of string can be a very helpful starting point, but ultimately you may find that you need to make adjustments as you go - so don't get hung up on the numbers.
3) Adjusting the saddle for intonation. For ukulele, this one is "kinda" adjustable, over a small range - across the width of the saddle slot, basically. Compensated saddles can allow a different effective scale length for each string by moving the contact point forwards or backwards relative to the center line of the saddle. If a string fretted at the 12th fret gives a different pitch than the same string played harmonic at the 12th fret, the intonation is off, and moving the contact point accordingly can help solve the issue. This is sometimes overlooked (or people will just always buy a compensated saddle, slap it on, and assume it's correct, without thinking about this as a possible "adjustment") but really, in my opinion, should be something that's adjusted as part of any setup. I say this because of the interactive nature of the variables involved. Switching string gauges will change the required scale length to have proper intonation, for instance. Changing the saddle height or nut height will impact intonation, as well, since doing so will mean the string is displaced a different amount when fretted. So once you know you have the action set up, you may find that a string is slightly out of tune at the 12th fret, and upon discovering that, you can file the nut one way or the other (or switch to a different pre-made nut) to get the intonation corrected.
People sometimes get intimidated by setups, but - ultimately - it boils down to knowing what the variables do, more than possessing any specific difficult technical skill or knowing any magic number to aim for. The actual technical work is pretty easy - filing or sanding some small bits of bone or plastic - and the best ways to do so are well covered all over the internet. The thing I find lacking is often a thorough explanation of WHY you should (or should not) make a specific adjustment, and how to know when you've got it right (versus just shooting for an arbitrary number). So I hope this helps with that aspect. If not, ask questions, there are lots of very knowledgeable people on this forum.
