In order to save some time and because I wasn't sure I could properly use a sander, I used a hardwood floor kit I bought from the home improvement store to restore old wood floors. I should mention that this method will not leave the floors looking like new, but I was pleased with the results.
I cleaned the floors thoroughly with the hardwood floor cleaner in the kit, and I mopped the floor. It took several hours to complete the cleaning part because I had to be sure not to leave any of the cleaner on the floor. I actually, got on my hands and knees and wiped the floor with paper towels and cloths.
After the floor was clean, it was time to apply the finish. Some people told me I should use an oil based finish, but I avoid oil based anything when I can find a similar product that is water based. The floor finish in the kit was water based, so that was good.
When I applied the first coat, the floor looked much better. Of course it had looked bad originally because it was dirty. I applied the second coat and the floor looked even better, and it shined more with the second coat. I could have added a third coat to get more shine, but I preferred to stop at two coats.