How can I find out what's clicking on my bike?
First of all, welcome to the "mysterious click" society!

The obvious first thing you want to check if this is pedal or not. Find a certain way to reproduce the click and reproduce it by pressing on the pedal, its furthest end, only. Then try to reproduce by pressing only crank by your foot using similar force (be careful, cranks are slippery!) and watch what happens. If click does not happen, then there's a good chance all you need is to tighten your pedal a bit.

If the click is still happening, check the screws on your stem and handlebar, saddle, also check if quick release levers are tight enough. These can click if too loose too. If you have a threaded stem, tighten the center screw - it does click if loose.

It is usually very hard to understand from where exactly the click comes. Try to apply the pressure without grabbing handlebars, try all kinds of tricks to understand what is clicking.

Carefully check out all the frame and cranks for cracks. Those can happen on new bikes too. Check your chain - may be there is a loose link?

If the click still happens, then it is a bit more mysterious than the usual causes. I have had a bike which was so mysterious so that even LBS disassembled it all and re-assembled for free - the click was gone that way. Reason still unknown.