Think of it like this. Whenever you end up at a showdown you have to make your best 5 cards from the 7 available (5 on the board, 2 in your hand) and so do each of your opponents. For simplicity sake we'll say you're against one other person. First you have to classify what you have, ie. high card, pair, 2 pair, trips etc. If that classification beats your opponent (ie. trips over his pair) then you win the pot, easy.
EXAMPLE: You hold Qc8s hole cards, opponent has Qd9h
Board cards: 7s 7c Jh 3d 4c
your best 5 cards: 7s 7c Qc Jh 8s
opponents best 5 cards: 7s 7c Qd Jh 9h
In this example you both have the same (eg. both have a pair) so you look at how high the pair is. If you both have the same pair (eg. both a pair of 7's) then you look to the next high card, in this case a queen for both of you. So you go to the next, the Jh and still the same for both. You then go to the last card and your opponent has a 9 while you have an 8, therefore your opponent wins.
If the board had an ace on it instead of the 3d then it splits as you both now hold the same 5 cards.
In the case of a flush, you take the 5 cards to a flush that you have and compare to an opponents. If you have, say, AQ432 flush and your opponent has KJT86, you win as you have an ace high while he has king high.
Make sense? I'm usually terrible at explaining things so I hope it helps in some way!
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