The chords you need are Dm, Am, and E, while the lyrical content is all up to you. The first option is to find Chastushka tunes, while the second one is to be original and come up with your own stuff.
Here's a nice example:
Dm AmJust keep in mind that the song is supposed to be satirical, humorous, or ironic, have a few drinks, and get the party started.
Down the river drifts an axe
From the town of Byron
Let it float by itself-
Fucking piece of iron!!!
You can watch a demonstration video below, or check out the tab here.