The first line of the description on the page you link to says "The Soundcraft COMPACT 4 mixer is perfectly suited to many applications requiring simple mix facilities, but it comes into its own when used for recording vocals and music onto computers using a soundcard."

there's a little clue for you ;)

Connections

Hey Paul, The best way to look at connections is to think about the signal flow. There is the gointo and the goutof. First go to your PC and locate the sound jacks. They will either be on a card or part of the PC's mainboard. Sometimes they are color coded:
Pink= mic
Lime= audio out
Blue= audio in
If they are not color coded they will have a symbol etched on the plate showing the signal direction. This is indicated by a half circle with an arrow pointing in (input) or arrow pointing out (output). TOO PREVENT DAMAGE it is BEST TO CONNECT OR DISCONNECT CABLES WITH THE PC AND THE MIXER POWER OFF.Once you have identified the jacks on the PC then look at the top of your mixer. There is L/R jacks labeled Record Out. This is the output of the mixer and uses either RCA jacks(unbalaced) or 1/4" phone jacks (balanced). This is where you connect the output of the mixer to the input of your soundcard using the RCA jacks (unbalanced). To do this you need to purchase a stereo RCA plug (red/white) to 1/8" stereo mini phono plug cable. This can also be made using a standard RCA stereo to RCA stereo cable and a RCA jack to 1/8" stereo plug adapter. you can pick this up at Radio Shack or most places where the sell stereo equipment. You can monitor the input signal at the mixer with headphones. Monitoring is useful when setting mixer volume levels in conjuntion with the level meters on the mixer.

Once you have things connected you need to make sure that the PC soundcard LINE IN option is enabled. To do this locate the little speaker icon in the system tray at the lower right Windows desktop. then right mouse click and select "Open Volume Control" from the pull down menu. From this window make sure the LINE IN volume control is present and the "Mute" box is NOT checked. The volume slider can be adjusted for the desired input volume. If the LINE IN is not seen in the window, click on the "Options" button at the top left of window and select the "Properties" option from the pull down menu. From the Properties window click the "Recording" option an this will bring up a list in the field below. Select the LINE IN box to add it to the volume control window. Select the "OK" button to save the setting. Then proceed with the adjustments as described before.

If you don't have it already you will need a Multirack Recording program to record down your music. This a list of a few free ones:
Digidesign Protoolsfree
Kristal Audio Engine
Quartz Audio Master
Anvil Studio
Audacity
You can use these to test your system out and get familiar with the recording process. It would be helpful to read your mixer manual in order to become familiar with how to connect your instruments to it and how to control it. In addition, I would try to do a search on "Digital Audio Recording" and research as much as you can because there a lot of aspects to recording on a PC that you should know.:D
Hope this helps and Happy Birthday!!!!