Programs take longer and longer to load. Hard drive runs even when you are not accessing it. Files appear on your computer with strange names that you don't recognize. Strange graphics appear on your computer monitor. Your conventional memory is less than it used to be.
Programs act strange or erratically.
This is not to say that your computer has a virus if it displays one of these symptoms. There may be some other problem causing the behavior. The above examples are just some common indicators of a virus.