J comedy has been a challenge for me for a while, but in recent years I've made progress. For starters, I'm a fan of よゐこ (Yowiko)'s Arino Shinya, the star of Game Center CX. Highly recommended if you like video games!
There's also an older comedian named Shimura Ken who has done some pretty funny stuff throughout his career, and much of it can be found on YouTube. Although some of it may be a bit challenging depending on your level of Japanese, I think some of his skits are simple enough to be enjoyed regardless.
I know YouTube videos are often here today and gone tomorrow, but for now here are some examples of his stuff.
First, this is the first Shimura Ken skit that I saw, and as a former ALT it really hit home. I've since shown this to several Japanese people who attested to its accuracy. A good entry point!
Next, here's a series of skits (there are two videos on YouTube), where he plays a salaryman coming home and being greeted by his wife, who is played by a different woman (mostly) in each one:
Here's one where he plays an incompetent ninja:
He also has a number of routines where he plays a pervy guy trying to cop a feel. Here's one such:
I think Shimura Ken is a great introduction to J comedy, though he may not be reflective of what's popular at the moment. Any comedians that you'd recommend?