Summarize:

Your deck should have exactly 60 cards and it should be shuffled well. One-fourth to one-third of the cards in your deck should be energy cards for a well-balanced deck, but whatever suits you is fine.  If you don't have 60 cards to play with and you're playing casually, ask your opponent if it's OK to play with less than 60 cards in a deck. Make sure you and your opponent have the same amount of cards in your decks! Flip a coin to see who starts. The first player cannot attack on their first turn. Take 7 cards from the top of the deck and put them aside, face down. Look for a Basic Pokémon in your hand of 7 cards. Basic Pokémon are represented by a box that says "BASIC" at the top of the card. If there aren't any Basics, shuffle your hand into your deck and draw another 7 cards. This is called a mulligan. Each time you perform a mulligan, your opponent has the choice of drawing an extra card. If you have at least one basic Pokémon in your hand, put the one you want to use for attack first face down onto the playing area a few inches in front of you. If you have more basic Pokémon cards in your hand, you can put them face down beneath your active Pokémon as your bench. You may have no more than 5 Pokémon on your bench at one time. You can look at your hand, but don't look at your prizes yet! Place these cards in a pile on the side face-down. Each time you knock one of your opponent's Pokémon out, take a prize card. When you run out of prize cards, you win. Fewer prize cards can be used for a faster game.  There is a special rule for EX and GX Pokémon. If you knock out an EX or GX Pokémon, you get to take two instead of one Prize Card. Contrary to popular belief, you do not take or keep your opponent's Prize Cards. Once you knock out a Pokémon, you take Prize Cards from your own pile, and put them into your hand. Typically these should be on your right side, opposite to the prize cards. Your Discard Pile will be below your deck. When you are ready to begin, make sure your active and benched Pokémon cards are all turned face up. The rest of your hand, prizes, and the rest of your deck should all be face down. You can look at your hand, but not your deck or prize cards. You win if you take all your prize cards, if your opponent has to draw but can't because they've run out of cards in their deck, or if you knock out all Pokémon on your opponent's field.
Shuffle your deck. Determine who goes first. Draw 7 cards. Find your Basic Pokémon. Pick your active Pokémon. Draw your six prize cards. Put the remainder of your deck to the side. Face your cards in the right direction. Play until someone wins.