Japanese humour takes many forms.
The most 'traditional' is rakugo, which is a man sitting in seiza (sitting on his legs with a straight back) and telling stories with different voices. It's not quite stand-up, but more like a monologue humourous story, or set of stories. The humour in it that I've seen used most tends to be about married life, or family life.
Another type is called 'manzai' which is two-person standup comedy, where one person plays an idiot of sorts and gets chastised and slapped by the other. Sometimes both are idiots. Sometimes there are three people. But basically it's a bunch of verbal jousting and slapstick tossed together. Think Abbot and Costello from the 1930's US.
Then there are one-shot comedians on the TV which generally have a gag/tagline which they use as their punchline for everything. For instance, the 'Guitar
Samurai' would sing a song about a famous celebrity and then make fun of them with the second verse... For instance...
kiyohara ha home run wo ippai utsu to iu no ha iin jya nai...?
kiyohara (Japanese baseball player) hits tons of homeruns, that's good, right...?
demo strikeout mo ippai kara ZANNEN!
But he also strikes out a ton! THAT SUCKS!
Or something of the sort. The format basically being giving a compliment (iinjya nai? - it's good, right?), and then following it up with a bad thing (ZANNEN! - that sucks!/unfortunate). Sometimes he'll even follow it up with '
seppuku' (suicide through self-disembowelment).
Other examples include HG (Hard Gay Razor Ramon) who dresses in all leather, screams 'FOO!' and does pelvic thrusts at random people on the street in the process of asking them if they would like his help with something.
There are too many to list, and they come in and out of style real fast (a 6 month shelf-life is pretty good for one of these guys).
I hope that helps.