Regular -er verbs

Most verbs tend to fall in 3 categories. Regular -er, regular -ir or regular -re. The regular bit means that the way you form the verb is very similar for most verbs in that category. This posts just for -e verbs like manger. Manger means to eat.

Je mange     (I eat)
Tu manges     (You eat)
Il mange        (He eats)
Elle mange   (She eats)
On mange     (one/we eat)

Nous mangeons  (we eat)
Vous mangez       (you eat [plural])
Ils mangent           (they eat)
Elles mangent      (they eat, where everyone is feminine)

The bits that have been highlighted represent the common endings. Whichever -er verb you have, you take the stem of the verb (in this case it's mang which is basically manger without the -er. For any verb, just take off the -er and you'll have your main bit). You then add the highlighted endings to the main bit depending on who is doing the action. Here's another regular -er verb, aimer = to like.

J'aime
Tu aimes
Il / Elle / On aime  (these have been grouped because they have the same ending)

Nous aimons
Vous aimez
Ils / elles aiment

See the similarities. The endings are the same (the ones in bold), they've just been added to the different main bit (or stem). Just like with manger, I've taken the -er off aimer to form the stem or main bit of the verb aim, which you then add the endings to.