Basically, tiers fall into descending order with the following groups:
Uber is the highest tier, while NU is the lowest. To determine which pokemon you can and can't use, then pick a tier, then you can use every pokemon that falls in that group, and all those below.
Example Team 1: Staraptor, Mismagius, Donphan, Nidoking, Suicune, and Togekiss.
This team has all pokemon fall under UU (Underused) so you can battle in the underused tier. Since they aren't too high, you could also use this team as an OU or even an Uber team if you wanted.
Example team 2: Serperior (OU), Mightyena-(NU), Slaking (NU), Pidgeot (NU), Masquerain (NU), and Unown (NU).
SInce you have a pokemon of the OU tier, you can't use this team in NU, despite a majority of your team falling in that tier. You would have to use this team in OU or Uber.
If these don't make sense to you, you can just remember this:
Uber-Just about Any pokemon can be used here.
Overused-any pokemon except those listed under "ubers" can be used.
Underused-Any pokemon except those listed in Ubers, or OU can be used here.
Rarely Used-Everything except those listed in Ubers, OU, or UU can be used here.
Never Used-You can only use the pokemon listed in this tier.
Don't forget you can also use any not fully evolved pokemon like Quilava if you wanted. If they aren't listed on the tier list, then assume they are NU, meaning you can use them wherever you want.
If you have a problem with a pokemon being listed on a tier, then you are more than welcome to challenge a tier and propose a change here. The tiers are also just to make sure every pokemon can see a bit more use. Without them, we'd just have Arceus and the other major legendary pokemon running around everywhere, so they're kind of a necessary evil. If you wanted, you could use a Kecleon in the uber tier; as long as a pokemon doesn't fall too high up the tier list, you can do it.
The tier list itself is right here for your viewing pleasure.