Install and start the VNC server on your Raspberry Pi
We're going to start by installing tightvncserver. Open a shell on your Raspberry Pi and type:
sudo apt-get install tightvncserver
After this completes, go ahead and start the server.
This will prompt you for a password, so enter one you'll remember.
Now we just need to grab the IP address of the Raspberry Pi and save it for later. To get the IP address type:
Since I'm using a USB WiFi adapter, I'm looking at the inet addr on the wlan0 interface (192.168.1.243 for me).
Install and set up a VNC client
You can install the VNC client of your choice. I'm going to use Chicken of the VNC (for Mac) since that is what I'm familiar with and because it works well. If you're using Windows, a quick Google search can find you another good VNC client.
Once this is installed, open a new connection using using the IP Address of your Pi as the Host address, enter your password, and use 1 for the display. Then connect.