The rules:
http://www.avalonhill.com/rules/diplomacy.pdfAlso, skim over this thread. I posted a very basic summary of the game on pg3, and posted a bunch of helpful strategy links on pg2. I'd read my summary on pg 3 first, then read the rules, then read some of the strategy links.
To answer your questions:
Supply Centers (SC) are the objective of the game. Control more than half of them and you win. SCs get you builds -- for every SC you control, you get to build a new army or fleet in one of your home SCs. Lose one and you'll have to disband an army or fleet. Basically, your SCs = # of units on the board (with some exceptions).
Fleets are your navies, armies are your armies. Fleets can move on water or on coastal territories. Armies move on land only. Armies can move over water if they're convoyed by a fleet (see the convoy order in the rules), or they can move across the dotted lines you see on the map without the aid of a fleet.