When you play Pyramid Solitaire, you are attempting to match up two cards that have a sum total of 13, so you can remove them from the game. You can only remove cards from the pyramid that do not have a card overlapping them.
At any time if you can't find a pair of these cards, you can click the deck at the top right of the game screen. This will give you another card you could potentially play.
An obvious example of a pair you can make is 10 and 3 (10+3=13). Other ways you can make pairs include a Queen and an Ace (The Queen is worth 12 and the Ace 1) or Jack and 2. You can remove a King from the game without pairing it up with any other cards because the King is worth 13 by itself. You win when you've removed all the cards in the pyramid from the game.
Spider Solitaire is a classic solitaire card game played with two decks. You try and build the cards into columns going from King to Ace.
Scorpion Solitaire is a little like Spider Solitaire. In Scorpion you can grab the column of cards from any card within the column. Also the cards never disappear.
Spiderette Solitaire is a single deck version of Spider Solitaire played with only 7 columns instead of Spider's 10 columns.
Classic Solitaire is the world's most popular solitaire card game. If you're only familiar with one solitaire card game, it's probably Klondike.
Freecell is a classic solitaire card game where you can move cards between the columns, or into freecells located on the top left of the game screen.
Gaps is a great little solitaire card game where you can move cards into gaps trying to arrange the cards into order by suit.
In Golf Solitaire you move cards out of the 7 columns and into a pile at the bottom of the game screen if the card in the column is one greater than or one less than the card in the pile.
Pyramid Solitaire is a popular solitaire card game where you try and match up cards that added together make 13.