I want to install a subwoofer because of the added bass. But, problem is, I have no idea where to start. How would I hook it up, what so I need, etc.

 

First you'll need to replace the stock head unit. There may be a harness on some units (idk), you'd have to check on yours. The stock PoS in my R53 did NOT.
This is necessary because you need a line-out for signal. Also behind the deck will be a low-guage remote wire. Basically the on-off with the deck.
These lines need to be run to an amp. The sub needs to powered by an amp unless you find something with an integral amp (bazooka, etc.). The amp will also require a power line (much heavier gauge than anything else) with an inline fuse. My R53's was super easy because it was super short (pos. side of battery to backseat). The amp will also need a ground.
Finally, run some speaker wire from amp to sub. Sub should be mounted in a box tightly and prewired to a quick-connect on the outside/back.
All the above is not to be confused with thorough instructions or a diy guide. There's already an exceptional write-up on how to change the head unit. Search is your friend. Also, a few minutes search (around the web) should provide ample pictorial/video instructions on each part of the above.
A typical shopping list would include:
1-Sub Woofer
2-Appropriate box (big enough to take woofer, shallow enough to fit Mini)
3-Amp (more valuable/important than the sub)
4-Amp install kit (on-the-shelf at your local big-box)
If your stock stereo needs to be replaced the list grows:
5-Stereo (you'll want something with sub-control as a feature, other options at your own discretion)
6-Mounting Basket and Wiring Harness (these are separate items that are both model/year specific)
7-Wire connectors (head-unit to new harness, then it's just harness(new) to harness(car, from back of stock PoS))

 

Start here, http://www.integralaudio.com/install...C1101S-R56.pdf

That's one way to do it.... (and what I have..)

 

I installed a sub in my '08 Clubman a couple of years ago. The instructions that richardsperry are essentially the same thing that I did on my installation, although I did not have the detailed instructions that he provided. They are really good!

If you are like me and you never installed a subwoofer before, you will find that this is quite an involved job. You have to remove the back seat, the rocker panel covers, the battery compartment cover, the kicker panels on the driver and passenger floors. This is required to run wires on each side of the car. One side for power to the sub and the other for the audio feed to the sub. It took me about 8 hours total, but WOW was it worth it! My MINI stereo system sounds amazing!