How to hook up a 5x7 LED matrix to Arduino?
A quick look at the datasheet shows that the individual LEDs are multiplexed, meaning that a single line can drive more than one LED.  In this case, all of the anodes in a column are electrically connected, and all of the cathodes in a row are electrically connected (or vice versa, depending on the model).  That means, whenever you manipulate a pin, you are manipulating that whole row or that whole column.  By choosing one column and one row, you can control an individual LED.  You can then manipulate all rows and one column, which will allow you to control a whole column at once.  To control all of them, you'll need to switch each column in sequence, changing which rows are active.  If you do this fast enough, it will look like they're always on.  This is called time multiplexing, or time-division multiplexing, since each column gets a slice of time in sequence.

Here's an example of a project that uses a 5x7 matrix and time mulitplexing:

http://heim.ifi.uio.no/haakoh/avr/

Run with that for a while, and come on back if you have further questions or add comments to refine the question.