How do vegetarians break down plant cell walls to obtain nutrients from plants?

They don't: Vegetarians are humans with the same digestive capacity as other humans. There are animals known as ruminants, like cows, that have an extra stomach in which bacteria help them break down the cell walls from plants like grass. People can't get nutrition from grass, even if they become vegetarian. Vegetarians eat fruits, vegetables, and plants that are edible to all humans.