A: Some malware do nothing until a triggering effect (specific time, amount of time since install, application launched, website visited, etc.)
Some take some action immediately.
Well-designed malware will never present evidence of their presence to the user. This is to say, if you see suspicious activity on your computer, if it is due to malware, it was poorly written code.
The first line of defense is to install a quality antimalware utility. I currently only recommend Bitdefender.
The next step is to have your computer professionally audited to ensure there is no system damage, and that all security measures are in place.