I'm trying to learn how to play and I understand what community cards are, what they do, who goes first/last, etc, but how do the cards in your hand effect the game? I can't find the answer anywhere and it's getting confusing.
You make the best combination of your hole cards and the community cards. So if you have Ah Ad in your hole cards and the community cards are 10h 6d Ac Ks 2s, you're hand is Ah Ad Ac Ks 10h.
An important note is that you do not have to use any of your hole cards. If the community cards are A K Q J 10 of Spades, then your hand is the same the community cards (along with everyone else). In this case you do not use your hole cards at all to make your hand.
It's quite funny when it happens that the table makes the best possible hand. Everyone still in shows what cards they were bluffing with and splits the pot.
I've had it where I was winning until the final card caused one of these split pots; I'd been betting strong and was hoping no-one would notice that the table held the nuts (they did).