Right, well... it sort of depends on the problem with your desktop. If it was indeed the hdd, then you will have to go through a more lengthy process.
Assuming the hdd is ok, it's still not going to be easy. You can't just hook up your drive as a slave in your laptop. You're going to have to buy an external enclosure to accomidate your 3.5" hdd and connect it via USB to your laptop.
In this case, you will be able to hook up your drive through USB and just see it in "My Computer" as you would a regular flash drive. This way you should be able to pull everything off.
If this is NOT the case and your hdd is bad, you will have to run a program, such as getdataback or something of the sort, to pull all of your information off.
In either case, you'll need an external enclosure. If you have another *working* desktop computer laying around you can use that instead...