There is a popular joseki here that's often one of the first ones people learn, though there are plenty of subtleties that can make it interesting up to much higher levels. Here it is:
$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . 1 . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 6 5 O . . |
$$ | . . . . . . . . . . . . . . . 2 3 . . |
$$ | . . . , . . . . . , . . . . . 4 7 . . |
$$ | . . . . . . . . . . . . . . . 8 . . . |
$$ | . . . . . . . . . . . . . . . . 9 . . |
$$ | . . . . . . . . . . . . . . 0 . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . 1 . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 6 5 O . . |
$$ | . . . . . . . . . . . . . . . 2 3 . . |
$$ | . . . , . . . . . , . . . . . 4 7 . . |
$$ | . . . . . . . . . . . . . . . 8 . . . |
$$ | . . . . . . . . . . . . . . . . 9 . . |
$$ | . . . . . . . . . . . . . . 0 . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
...after which black plays x, but I don't know how to make a 10 stone. (Edit: 10 added, thanks Bill!)
So...why this sequence?

: If white plays on the other side, black plays here and the corner is under attack. If that happens then white is too weak to cut black so he has to play submissively to live/connect small, and black easily makes a strong shape that may be useful thickness.

: Black chooses this one because it presses white in a way he cannot usually resist strongly. His goal is to make his stones strong, so he wants to find the most powerful way to lean on white and do so.

-

: White can't push and cut as black will get a powerful turn and attack white before white can attack black, so white plays the best moves available to become alive. Black is happy to be pushed from behind, so he lets white do it.

: White is no longer pushing from behind so black settles his shape and stops white pushing out and making him potentially weak.
So the basic result is that black gets thickness, white gets territory. The position is still quite active and both players have moves to aim at. For instance, black can play the 3-3 in the top right, or play forcing moves against white's group on the side which may die if he isn't careful. Meanwhile, white can aim to cut black by wedging in as below:
$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . O . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . 1 . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . . . X O . . |
$$ | . . . , . . . . . , . . . . . X O . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . O . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . 1 . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . . . X O . . |
$$ | . . . , . . . . . , . . . . . X O . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . O . . |[/go]
So those are the basic ideas, but I'm sure you've already thought of many questions or confusions about all of them along the way. As you say, the board is quite open and it would seem that along the way there are many choices both players might prefer to make differently. Nevertheless, for good reasons this sequence is by far the most popular.
As discussed in the other joseki thread, I suggest looking through and wherever a move is confusing or not obvious try to find those reasons - and feel free to ask! The exact sequence is not important to know or to learn, but if you get a handle on the good reasons for playing each move you'll understand more about this joseki and many others.
Edit: And of course, there are other joseki both players could try, but this one is by far the most common once black has jumped out - essentially, the jump by black is a declaration that he wants thickness. If he didn't want thickness, he might have played differently, such as playing a double approach or the 3-3 point instead of the jump.