I'm using a 1990 325i convertible as a reference point, because that's closest to your car. In the back of your owner's manual, they might specify the belt sizes for you (I know they do on the 90 and 91 E30s)
You're guaranteed to have at least two belts (alternator/coolant pump) and power steering, while AC is a popular option. Figure $20-30 total from autozone or similar auto parts store.
Next on board are tools. Socket and regular wrenches in 10 mm, 13mm, and 19mm (for the alternator) are mandatory. A drop light, jack stands, safety goggles, latex/rubber gloves and a functional floor jack are highly useful. Reason being is I have to work from above and below the engine, and getting dirt and grease specks in an unprotected eye is frankly not a lot of fun.
Then it depends on your sense of adventure and tolerance for working in tight, dirty, and greasy spots. Finally, if you employ a jack and stands, you have to pick your lift and support points correctly, or you can do a world of mechanical hurt to your car. If that hasn't discouraged you, read on....
1. Get a good manual with plenty of pictures and explanations.
2. If you have a digital camera, take pictures and notes as you go along.
My approach in my garage:
1. Get and confirm I have the right belts and tools.
2. Set the parking brake, and chock the rear wheels.
3. Break loose the front wheel bolts to the minimum extent. Prayerfully the tire shop or brake mechanic did not go beserk with an air impact wrench and you will be able to do this.
4. With the floor jack, I put it under the cross-member immediately behind the oil pan, and raise the car.
5. I set the jack stands on the support rails behind the wheel wells and inboard from the doors, and lower the car onto them.
6. To make it easier to remove the splash guard, I remove the front tires. There's a side benefit of being able to check the disc brake pads.
7. I undo the splash guard (it's all one piece) from both wheel wells and set it and the retaining nuts and screws aside.
8. If you're certain you have the right belts, you can use a pair of diagonal cut pliers to cut the belts off. If you're unsure, find the nut/bolt combo that has a toothed gear, and loosen it only enough so you can take the tension off the pulley and ease the belt off.
9. On the 90, the order of removal is from the front of the engine toward the back, or power steering, AC, alternator.
10. Once all the belts are off, you can take a moment to look for fluid leaks, tears in the rubber boots on your steering rack, and the like.
11. Starting with the alternator belt, thread it over and behind the engine fan and set it on the innermost pulley. Once it's on correctly (as in seated in pulley and not twisted, turn the toothed bolt until you take out the slack and then some, then tighten the nut behind the support bracket to hold everything in place. A reasonable rule of thumb is a half-inch of deflection at the midpoint between the alternator and coolant pump pulley.
12. Repeat step 11 for the AC and power steering pump belts.
13. If you think you nailed it, you could start the car and check by sight and sound that your belts are on the right pulleys, not flopping around, and that they're running quietly. If all is OK...
14. Stop the engine, replace the splash guard, and put the front tires back on. Snug up the wheel bolts so you won't have much tightening left to do.
15. Jack up the car to get clearance to pull the jack stands, then gently lower the car until the tires have reasonably firm contact with the ground. Tighten up the wheel bolts in a staggered pattern to specs with a torque wrench, or good and tight if you're doing it by feel.
16. Go for a test drive after you're reasonably cleaned up to check your handiwork.
It took my son and I four hours the first time, because of unfamiliarity and the extra caution and trial-and-error. I'd be quite a bit faster now.
Advantages of this DIY:
You get that much smarter with the basic workings of your auto.
You take the opportunity to get quality tools you can use for other jobs.
You catch things before they become major breakdown issues.
Your car isn't tied up in a garage for an extended period of time.
Satisfaction of a job well done and money saved.
Initial growing pains of acquiring tools, sourcing parts, and doing the deeds.
Potential to screw things up big-time if you're careless with the floor jack.
On the excitement meter, this is up there with pulling weeds from the lawn.
Hope this helps at least somewhat.