I didnt really start using partyfinder until id been playing the game for quite awhile. When i started using it, i found it really helpful and set a hotkey for it. Now whenever im in game if im not in the process of doing something in any given second i compulsively click that hotkey to see what content people are putting groups together for so i can decide if i want to jump in(either to help or because i want to do the same thing). Ive laughed at myself for opening PF, not seeing any groups i like, closing PF, then immediately opening it again to see if anything new was posted. The mechanics are basically as Heul described. Open the interface, look at the groups to see if what you want is already there, hit recruit if it isnt, pick a duty, type a description, and open recruitment. Theres a bit of skill to writing a description that gets the group you want(a skill that improves with practice), but being lucky and having other people want to do the same thing at the same time helps a ton.

To get more specific about the unsync option(Heul appeared to run out of time while typing), this is one of the party customization settings you can use. An unsynced party is one who goes into a duty at their full normal level, with all attendant gear and skills available to them. Many PF groups prefer the unsync option(some content is almost always run in this way), but it isnt required. To set the option you actually go into the duty finder interface. The top left corner of said interface should have a button that looks like a gear on it. Pressing that gets you into the custom settings for DF. You can set unsync on(default is off). You can also change the loot settings for the group(theres normal, greed only, and lootmaster) and set min ilvl on(the opposite of unsync - it syncs you to the lowest ilvl to run the content for more challenge and sometimes more loot) from the same place. I dont typically advise messing with loot settings, as many people are unwilling to join a group that doesnt have the default set(ive personally noped out of lootmaster groups for content i didnt want any loot on). Any special settings like unsync, min ilvl, or loot preference should be mentioned in your PF listing(to make sure the people who join are willing to go along with it).

So once your PF group fills up, you actually still use duty finder to enter the dungeon/trial/raid. Blue's cant join matched parties, but a pre-formed party doesnt have to follow the normal rules. And one specific word of blue-related advice. Im under the impression(if this is wrong, someone feel free to correct me) that skills are easier to learn when you run content synced rather then unsynced. You get the clear with less effort going in with some level 80 friends, but you might have to go several times before you actually learn the spell. Most(all?) content for BLU that i ran at level, i learned my skills the first time i saw them used. Just something to think about.