I would say that in the vast majority of virus cases you will know right away that you are infected. This is because most viruses will block your internet access by activating a proxy or by preventing executable files from being run (such as programs and malware removers). Effectively, without online resources or the recourse of running an anti-virus, most viruses will leave you unable to act against them.
Some other viruses are designed to trick you into paying the author money to remove the malware they got onto your computer. To that end, these rogue “anti-virus” programs needs to be visible for you to act on them. They pop up with a window showing a virus scan in progress which is picking up hundreds of malware items. These reports are fake and you should not act on them.
Any unexpected pop ups or strange changes to your computer will alert you to the possibility of an infection. Sometimes ads will open non-stop or your background will be changed to something silly. In more severe cases, all of your personal documents will disappear from your computer and appear to have been “deleted.”
Remember that unsolicited changes are a sure sign of some sort of problem. Unless your favorite program just received an update and is now acting up because of it, the error messages on your computer are probably accurate. Simply contact a professional to have your computer cleaned up. Always have your anti-virus running and keep your subscription active with daily updates!