How long until you can get a STD test done after you have been exposed?

How long do you have to wait before you get tested when you have been exposed to a sexual transmitted disease?

I am sure there is an incubation period where even if you have been exposed it will not register on the test.

Also I am sure different STD's require different wait times. Like HIV may need a longer period before it can be detected in a sample than saw Gonorrhea.

If I get a full panel of tests for most type of STD's how long should I wait before testing? Days? Weeks? Months?