Translation:I drank too much at the party.
You don't use desu.
To start off, I'll use the base form of the verb, 飲む (のむ)。
Next, I'll convert it to polite form: 飲みます。
After that, I'll erase the "masu", leaving me with what is called the "masu stem" form of the verb: 飲み。
The auxiliary verb, 過ぎる (すぎる), is then attached to the masu stem. So the verb becomes 飲みすぎる。
Note that when the auxiliary verb "sugiru" is attached to masu stem of a verb, the newly formed verb becomes an Ichidan verb (meaning, the -ru part is dropped when conjugating it).
Finally, we have "drank too much", or 飲みすぎました。
arcferrari is right. the verb 食べる + the auxiliary すぎる should indeed become 食べすぎます in its formal non-past conjugation.
you probably saw 食べすぎです in another exercise. I think it would be literally translated as "(I'm) an overeater" instead of "(I) overeat". literal translation is surely not the best but it might help understanding some structures of a language.