How do I install my cartridge?

It may be worth it to employ the services of your local stereo dealer, at least if you don't have a knowledgeable buddy.

Having say that, some basic tools and the instructions go a long way. YouTube features videos on cartridge mounting. You may wish to seek help from fellow member who live in your area.

... and I don't have a screwdriver. Do I need one?

Normally yes.
But it is possible that yours is Sirius compatible, did you try to give an order via iPhone4s: "Mount yourself"?

Glen makes some great points. I definitely recommend getting someone more experienced to show you the ropes.

Another invaluable tool is www.vinylengine.com - they have alignment protractors that you can print out and tons of advice. Just make sure that you pay attention to the scale instructions if you use their protractors. It's a great free resource.