What can I use to clean inside my computer?

As an aside, the safest option BEFORE cleaning the computer is to completely discharge the computer. Any lingering electricity may cause a short circuit when attempting to clean the computer. To discharge the computer, simply unplug the power supply unit's cable from the power supply, switch the power supply's switch to the "off" position," and then press the power button one or two times. If there is still electricity inside when you press the power button, you'll see the computer momentarily turn on and then shut off as it loses the rest of the electricity.

The safest cleaning supply would be compressed air, though do note canned compressed air can condensate. This primarily occurs when the can is held upside-down.

Another often used cleaning material is 99.9% Isopropyl Alcohol, though more care is needed, especially near more sensitive electrical components such as the processor. It is capable of conducting electricity. The vapor is also highly flammable, so work in a well-ventilated environment and always let the components dry out before running electricity through them. Despite these concerns, it's commonly used because it is great at removing thicker types of gunk, such as dust or thermal paste, and it dries quickly.