Urine tests and blood tests and swabs. I actually see no reason for testing but I see a need for your BF to see a Dr asap.
Here is my recommendation...hold off on sex, your only 14. If you choose to have sex then you have to make adult decisions like using condoms and come with the potential consequences that comes from sex...STD's, pregnancy.
What kind of exams and tests do they give for stds?
I recommend that the both of you be evaluated and tested for sexually transmitted diseases by a physician. The symptoms your boyfriend is experiencing is not normal, and they sound quite serious.
However, the incubation period for Gonorrhea is 2 to 30 days, and Chlamydia is a bit longer, which means that it would take about that long before symptoms became present.
More info about that here:
http://std.about.com/od/overviewofstds/a/incubationper.htm