There are litterally billions of things you could do here. But here is a quick and easy thing to get you going.

By a Shure SM57. I recommend this because it's relatively cheap, can be found just about anywhere, AND is widely used for recording electric guitars. There are many other choices, but this is a great place to start.

Now you need a Preamp, and audio interface (for getting the sound into the computer) and software to record the sound.

Since you are just starting out, a simple preamp should do just fine. Something like the m-audio mobilepre which is a preamp/usb audio interface for the computer.

Then all you need is the software. Again, tons of choices here. If you want to learn a bit about recording you might want to look into some multitrack recording programs like cubase, cakewalk/sonar, etc. If you just want to record some audio just about any old audio recorder for the PC will work.

Go to your local music store and check out what they have. Some hardware companies bundle their audio interfaces with software so you can get it all at once.

Buy an amp simulator. With more than decent money you can purchase a Behringer VAMP.
Simply plug it in your soundcard and the result will be definitely unbelieveable. Just be careful with the level of the signal not to exceed 0 db.
You wrote trash? There will be a lot of.
Of trash of course.