Kabuki is one of the traditional theater forms of Japan, and is generally considered to be easier for us simple westerners to understand than Noh theater which is rather more stylised. In Tokyo the best place to see Kabuki is in the Kabuki-za theater in Ginza.
You can buy tickets online or at the theater, either for a full show or a single act. I went for the full show although I had no idea what it was about or whether I'd understand a word of it.
There are a number of distinct acts, first there's usually a short historical play, then a dance, then a comedy piece followed by the main play. You'll get a booklet in English with some information on the play you're going to see, and you can get headphones with commentary in Japanese, English and possibly other languages. I (perhaps foolishly) didn't bother with the headphones.
The first three acts were all easy to follow with a little help from the booklet and the lovely lady beside me who spoke about as much English as I spoke Japanese. The costumes, music and stylised speech were beautiful even if you don't understand them, and the dance was stunning with a beautiful young onnagata (a male actor who plays a woman) going through several lightning fast costume changes, each more sumptuous than the last...
The longer main play had a more complicated plot that I didn't fully follow, and it was long with stretches of dialog which were probably essential to the story. The headphones would definitely have helped here.
If you're interested in Japanese culture or in theater then this makes a most absorbing evening. If you'd like to have a look but don't think you could stick the four and a half hours of the full show then buy a ticket for one of the earlier, shorter acts, they're much easier to follow than the main play anyway. And do get the headphones even if you speak Japanese as the language used is somewhat archaic.