You already know how to use the arrow keys to move around the document. In addition, you can use the h, j, k, and l commands to move the cursor left, down, up, and right, respectively. This comes in handy when (for some reason) your arrow keys aren't working correctly.
The w command moves the cursor to the beginning of the next word; the b moves it to the beginning of the previous word.
The 0 (that's a zero) command moves the cursor to the beginning of the current line, and the $ command moves it to the end of the line.
When editing large files, you'll want to move forwards or backwards through
the file a screenful at a time. Pressing 
moves the cursor
one screenful forward, and 
moves it a screenful back.
In order to move the cursor to the end of the file, type G. You can also move to an arbitrary line; for example, typing the command 10G would move the cursor to line 10 in the file. To move to the beginning of the file, use 1G.
You can couple moving commands with other commands, such as deletion. For example, the command d$ will delete everything from the cursor to the end of the line; dG will delete everything from the cursor to the end of the file, and so on.