There are many ways to repair a slow computer, and there are many ways for a computer to become "broken" in a sense in the first place. I'll identify some common slow computer problems and some of the simple ways to repair a slow computer.
1. Invalid entries in the registry
Whenever you change a system setting or install a new application on your computer you're adding data to the systems registry. Over time this registry can become bloated with useless information as system settings become irrelevant or your uninstall applications. Find a suitable registry fixing application to repair this problem. A "broken" registry is a huge cause of slow computers around the world but is still easily fixed.
When components within your computer get too hot from over use or high stress your computer will become slow. The simple way to repair a slow computer that suffers form overheating is to allow for a greater airflow. Take your computer out of the corner of your room and place it elevated in a room with a window. Regularly clear the dust out of your computer and verify that your fans are operating properly. You can use the PC application 'Everest' to check the temperature of your computer components.
3. Corrupt operating system installation
In some cases unfortunately the installation of your operating system may be corrupt which can definitely make your computer a slow computer. The only real way to repair a slow computer with a corrupt operating system is to reformat it. Reformatting is the act of wiping your hard drive and reinstalling your operating system to start fresh. You can corrupt your operating system installation in a number of ways such as messing with system settings or installing dangerous software.