Cleaning kittens

I got a kitten from someone and he is about 6 weeks old.  He uses the litter box perfectly fine and he is totally happy and playful. He cleans himself a little bit but not so much "down there". Yesterday he pooped and it was kind of "diarrhea like" and then of course it got on his fur on his bum and he had no interest in cleaning it off. I cleaned him myself but I am just wondering at around what age do they figure this out for themselves?

Did the diarrhea look yellow-ish? 

It depends on the kitten. Some start with it really early, others are a bit slower and take their time before they start doing it. If he had a mom that did it for him until now, it's possible he never did it himself before and he expects his mom to do it. Eventually he'll realize he's dirty and start doing it himself as no one is helping him.

Yes, it was a yellowish/light brownish color. Not dark like normal.

It also happened again this morning. I think maybe I need to change his food? I am going to call the vet in a few. He hasn't been to the vet yet because I wanted to wait until I could get him his shots and stuff. But I might have to bring him in.

They learn all their 'social' graces between the age of 6-10 weeks, so mom most likely didn't teach him yet how to clean. You will have to teach him how to play nice and to get along with everyone too. If he has had a diet change that would cause a stomach upset too, and remember cats can get diarrhea from cows milk too, give him KMR, a kitten replacement milk found in the pet section or goats milk. All the luck!

XenaBean said:

 
Yes, it was a yellowish/light brownish color. Not dark like normal.

It also happened again this morning. I think maybe I need to change his food? I am going to call the vet in a few. He hasn't been to the vet yet because I wanted to wait until I could get him his shots and stuff. But I might have to bring him in.

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Was it okay before? If not, yellowish and rather soft (like glue-like) is what comes out when they have their first few days of alone-poo'ing, without help of the mother. Because the mom isn't licking it up anymore, you'll find it and it's like a weird yellowish kind of color. If he wasn't used to regular food yet, and didn't poop on his own at his old house, you are now seeing his first steps towards becoming a big kitty.

If this is the case, the yellowish stool is very greasy; it'll stick to his butt and no matter how much your kitten cleans it, it'll remain dirty-looking. This stool will soon turn for the better (normal brown and harder) and he won't have such a hard time cleaning it up anymore.

If, however, he had okay stool before or had okay stool at his previous home where his mom no longer helped, then you should do something to make sure his diarrhea stops. A kitten shouldn't have diarrhea for too long, as it can be dangerous for him. So make sure you know what kind of diarrhea it is.