About how often should a cat be using the restroom?

At least times 2-5 a day depends on breed and diet.

Urinations or bowel movements? Every cat IS different, but a missed BM is slightly less important than no/increased urinations.

Is there something specific you are worried about?

Well I got my cat a few days ago and I haven't seen him pee yet. Does kitty litter always bunch up when it gets wet? I think he may have peed because the litter is a little bit darker but I'm not sure. He takes in enough water so I was just wondering. He has a bowel movement at least once a day

It sounds like he has peed at least once. If he's eating and pooping (and using the litter box), I wouldn't worry yet. Does he seem uncomfortable or does he hide or act twitchy?

It really only clumps if you are using the clumping type of litter. If it is just darker and there's no poop there, then that's most likely urine.
I agree-if he is still eating, drinking, acting normally (i.e. not hiding or going in and out of box frequently or vocalizing in box) then I say he's most likely okay.
To be safe, you can check the type of litter you have and see if it clumping or not. And to be extra, super-duper safe, take a whiff of the box. Cat urine smells like ammonia and if he's peed a couple of time, I promise you you will smell it!

OK thanks yeah he is a pretty active cat and loves to be around us. We just adopted him from a local shelter and so I just wanted to know how often they go. He is a good eater and we have to fill his water up almost every other day