What you can and can't do with a file, as defined by your username or group name, is pretty much wrapped up in four little letters. Look at the following listing (using ls -l) for an example. The permissions are at the beginning of each line.
-rw-r--r-- 1 mgagne mgagne 937 May 17 13:22 conf_details -rwxr-xr-x 1 root root 45916220 Apr 4 12:25 gimp -rw-r--r-- 1 root root 826 Feb 12 09:43 mail_test -rw-r--r-- 1 mgagne mgagne 44595 May 17 13:22 sk_open.jpg
Each of these letters can be referenced by a number. They are r, w, x, and s. Their numerical representations are 4, 2, 1, and "it depends." To understand all that, you need to do a little binary math.
Reading from right to left, think of the x as being in position 0. The w, then, is in position 1 and the r is in position 2. Here's the way it works:
To specify multiple permissions, you can add the numbers together. If you want to specify both read and execute permissions, simply add 4 and 1 and you get 5. For all permissions (rwx), use 7.
File permissions are referenced in groups of three rwx sections. The r stands for read, the w means write, and the x denotes that the file is executable.
Although these permissions are arranged in three groups of three rwx combinations, their meaning is the same in all cases. The difference has to do with who they represent rather than the permissions themselves. The first of these three represents the user, the second trio stands for the group permissions, and the third represents everybody that doesn't fit into either of the first two categories.
The commands you use for changing these basic permissions are chmod, chown, and chgrp.