On the computer you wish to access remotely, download and install the Tight VNC Server. When you launch the server, you will be given a user properties screen.
There are a few options that are important here. On the Server tab, make sure that Accept Socket Connections is checked, and that you have a password set that you can remember. Under When Last Client Disconnects, make sure Do Nothing is selected, unless you want your remotely controlled computer to shut down after you've severed a remote connection. Also make sure that Enable File Transfers and Remove Desktop Wallpaper are checked.
On the Display Tab, you'll have the option to limit what parts of your PC can be remote controlled. Keep this at Full Desktop normally, unless you intend to have multiple users accessing the remote PC, and you want to limit their access to certain areas of the computer.
On the administration tab, make sure Disable Empty Passwords is checked, in order to increase security. You can also adjust how you want the server to handle multiple connections. Refuse Concurrent Connections is acceptable in most cases, unless you for some reason want multiple users to remotely log into your computer at the same time, in which case Automatic Shared Sessions can be checked.