I see people doing reps of 8, 10, 12, and even 15, but I'm not sure what the difference is in the amount of reps you do. Can anyone help? How many reps should I do in my lifting exercises if I want to build muscle?

The amount of reps you do depends on your goals.
If you are looking to gain strength and power, you should do 4 to 6 reps.
If you are looking to build muscle you should do 8 to 12 reps.
If you are looking to gain endurance, you should do 15 to 25 reps.

No matter how many reps you are doing, you should always use a weight where on your last rep, it is really hard where you feel like you are about to fail. So, if you are looking to gain strength and power, you will be using a heavier weight for your 4 to 6 reps compared to if you are the same person looking to gain endurance, whereas you would be using a lighter weight.

How many sets you do also depends on your goals.
1 to 2 sets are for people looking to improve general health and for beginners.
3 to 4 sets are for people looking to build muscle, burn fat, and are intermediate to advanced.
5 to 6 sets are for endurance builders, fat burners, and advanced bodybuilders.

I hope that helps!