How can you unknowning install malicious code on your computer?

Many things.

It can delete or damage files, and in so doing, destroy your personal files or your operating system. It can also overclock you processor to the point of failure or destroy it in other ways. It can also wear out Flash Memory or even RAM by sending excessive read/write commands for long periods of time, but this in not a common attack.

The most common in what I first mentioned: File manipulation. This is usually done to destroy your operating system.