How do you decide commendations?

Its completely situational, though a tank is more likely to get a commendation from me they are also more likely to not if they derp since I catch that faster than I do with dps.
If a dps does something which I see and is awesome they are incredibly likely to get a commendation, for example the monk dropping mantra at the perfect time for my aoe heal just makes me fall in love with them; also if I derp with my mana consumption and a bard actually notices me as a scholar derp up and using a ballad will get a commendation and an embarrassed thank you.

Personally I pick my player commendations by people who do their jobs well, and are party players. I mostly commendate the tank since theyre the ones usually pulling the agros off me as a healer allowing me to either holy or cure people without constantly having to keep myself alive though I don't mind doing so, its hard to keep everyone alive if your healer is being attacked by 6 monsters at a time. If a tank does this well I tend to commendate them by that. Then there are DPS who can do the same thing and play very well. If I see a DPS doing such I'll end up commendating them instead.
I also don't like it when people don't give new people the chance to view the cutscenes in the dungeons and get mad at people if they mess up for the first time. It's a game and mistakes allow people to get better skill at playing the game, we should be encouraging not negative towards new players.

I prioritize who gets mine usually.

1. The least ignorant one of the three/seven others.
2. Most helpful to newer players.
3. Only one left if I was still looking at final gear and i was spacing out lol
4. Most efficient with class played. I.e. tank didn't pull more than party was capable of going up against, dodging when needed, mitigating/aggro holding correctly. Healer was able to keep everyone alive through SR pulls or oh shit aoe moments (don't kill spiney), esuna,/leeches properly, has the ability to dps while keeping party alive, and dps class - simply kill things in the order they need to or when they spawn, dodge everything possible, take aggro from healer if tank isnt and use lb effectively whether it's bards, melee single target, or mage aoe.

oh and instant commend to the last one standing getting that last hit in so we don't have to fight the boss again!

I'm a healer, so usually if its a good tank or other good healer they will get it. IF its all DDs whoever did their job well, and died the least gets my commendation.

I try to give mine to the person I feel deserved it most. This includes being knowledgeable, helpful, and preformed with their job the best. If I can't decide based on everyone doing an equally good job, I'll almost always give it to a DPS. We all know very well that Healers and Tanks get the commendation 90% of the time, so I try to spread the love to the underappreciated!

For me, if I see a DPS utilizing skills outside of their DPS rotation, like a caster using either virus or eye for an eye, they'll get it, or a melee who doesn't need to be told to LB every boss, or even just paying attention and not getting hit by avoidable aoes/getting on adds asap. Otherwise, if it's a smooth run, it goes to the tank.

I tend to tank so I usually get one or two per run and I will admit I tend to go for healer first unless they were terrible then I go to the DPS. Sometimes DPS first if they were impressive and helpful. I noticed as I have been leveling my Arcanist that I often get 1 or 2 commendations per run as well. One time I got three in Tam-Tara Deepcroft and the tank died on the last boss I think due to healing error so I swapped to tank Carbuncle and we still pulled out a smooth victory, got I think three commendations for that.

In general in 8 mans I tend to either do the other tank or anyone that was helpful.

If person is friendly and helpful: commendation goes to him or her.
If all 3-7 party members were friendly and helpful...: someone gets it.
If everyone was a prick: no commendation for you.
If everyone was neutral (i.e. no communication): perhaps I may give someone one based on how little I have to heal them (cause I'm usually healing), but perhaps not.
And generally I'll try to give it to a DPS, but awesome people take priority.

If someone does something to stand out, I am more likely to see them as deserving of my commendation. For example, someone who goes out of their way to explain a fight will get my commendation. Likewise, good attitudes will get a commendation. Using a LB at a good time, or raising a party member when it's needed, or pulling some stunt that prevented a wipe... these are all things I notice. Granted, it IS hard to see when a DPS is doing a great job UNLESS they do something exceptional. Oh, and I do enjoy giving out commendations to people who admit they are new to a fight but open to advice. Even if they make a few mistakes, I think we should encourage honesty and good attitudes.

If it's a dungeon where people don't do anything exceptional and don't really speak at all, I'll usually throw it to someone who says 'thanks for the group' or something similar. If no one does that, it'll probably just go to someone random. I very rarely DON'T give out commendations, unless the group was seriously that terrible or rude.

If mobs are going and attacking everyone, then the tank failed.
if everyone is doing their job but the healer goes OOM then the DPS failed.
if the tank dies or a dps dies while the tank is at full health and the healer has mana then healer failed.

there are of course exceptions but in a nut shell this is a decent way to tell who isnt pulling their weight.