[verb ます-stem] + ません
From the dictionary form:
Like ます, it covers both habits and the future: "do not" and "will not".
In a negative sentence the thing not eaten or not done often takes は in place of を. Both are correct. は singles the thing out: not this, whatever else may be true.
Japanese picks the negative by the kind of word. A noun takes ではありません, an い-adjective changes い to くない, and a verb takes ません. The noun ending does not go on a verb.
These go beyond the basic polite sentence.
~ませんか is usually not a real negative question. It invites: "won't you…?", "would you like to…?"
~ません goes on the same ます-stem as ~ます.
With friends and family the negative is the ない-form: たべない食べない, のまない飲まない. ~ないです also turns up in conversation as a softer polite negative, but ~ません is the standard one.