Changing and balancing a tire is not a complicated process. It is easy to get right. However, even with tools it does take a good bit of elbow grease and without the fancy tools it can be downright frustrating.
There are tons of videos out there that will show you how (a couple already linked in this thread). Here are some of the things that can go wrong:
- Popping the bead can be extremely frustrating without a good tool to do it.
- Working the tire off/on the wheel using tire irons can be difficult the first time. Lubricating the tire edges with soap and water will make it much easier, but there is still a small learning curve on the irons.
- Old, stiff tires can be really annoying to get off the wheel.
- It can be easy to scratch the paint on the rims if you aren't careful.
- it is easy to bend the brake disks if you don't take them off first.
- You will need an air compressor to set the bead on the new tire. Sometimes a regular air compressor is not enough. For example, if you had your new tires shipped to you and they strapped the tire into a tube, the rubber might not make enough contact with the rim to form an initial seal. If this is the case you can spend a lot of time trying to get it to inflate or you can buy one of these ($180) and commit to changing all of your own tires to make it worth buying. In defense of the tool, it does work fantastically and is very satisfying to use.
- Getting the wheel back on can be done alone, but really it is a two-person job. Making sure the brake calipers, wheel spacers, and axle all line up properly without anything falling out of place can be an extremely frustrating to do alone, in my experience.
So yeah, easy to understand and get right, it just makes me wish I hit the gym more often.
Get yourself some tire spoons (a set of 2 is good), rim protectors (so you don't scratch them up), something to break the bead (bead breaker or large c-clamp) and some zip ties. Those will get the tires off and your new tires on. As for balancing, go to harbor freight and buy a motorcycle wheel balancer for like $40. It's cheap but it works, I've done 2k on my recent tires and hit triple digits and have not had a single problem. They sell wheel weights too but you might be good reusing your current ones.