[verb ます-stem] + ます
From the dictionary form:
A verb that ends in ます is in its polite form: たべます食べます (eat), のみます飲みます (drink), よみます読みます (read). The verb goes last in the sentence. This is the form to use with anyone you don't know well.
The ます-form covers habits and the future. Japanese has no separate future form – a time word such as あす明日 does that job.
The ます-form is not "is eating". An action going on right now takes ~ています.
These go beyond the basic polite sentence.
Whatever stands in front of ます is the ます-stem: たべ食べ in 食べます, のみ飲み in 飲みます. The other three polite endings go on the same stem, and so do ましょう (let's) and たい (want to).
A dictionary lists a verb in its plain form, the dictionary form: たべる食べる, のむ飲む. It is also what you say instead of the ます-form with friends and family. How it turns into the ます-form depends on which of three groups the verb is in.
Ichidan verbs (v1) end in an い-sound or え-sound plus る. Drop the る and add ます.
Godan verbs (v5) change their last sound from the う-row to the い-row and add ます.
The two irregular verbs are する → します and 来る → 来ます (read くる and きます).
Some godan verbs end in る after an い-sound or え-sound and look like ichidan verbs: かえる帰る, はいる入る, はしる走る, きる切る, しる知る. They keep the る and change it to り.
The same slot takes the other polite endings: ません (does not), ました (did) and ませんでした (did not). Each has a point of its own.