There are many ways to do that, and some methods depend on whether you are switching AC or DC. The amount of current you are switching is a factor to consider in any method. How you wish to control the switch is also a consideration, whether manually with a pushbutton, for example, or remotely with a trigger signal. Too many variables left out in your post, but you may want to search on time-delay relays. Also, it's not clear whether the switch turns on after the delay or off after the delay.