The verb groups are based on the infinitive of the verb (its form when it’s not conjugated, the one you can find in the dictionary), and for the second group, also it’s form with “nous” at the present time.

The first group : the verbs ending in -er at the infinitive, except aller (third group).

→ marcher, regarder, nager…

The second group: the verbs ending in -ir at the infinitive, and -issons with “nous” at the present time.

→ finir, choisir, réussir…

nous finissons, nous choisissons, nous réussissons.

The third group: every other verbs!

→ boire, ouvrir, prendre…

Avoir and être are appart. They can be considered like belonging to the third group, or as auxiliaries and not belonging to any group, depending of the sentence.

J’ai un nouveau livre. I have a new book. Here, to have is used as a verb, it is third group.

J’ai vu ce film. I saw this movie. Here, to have is used to conjugate to see at the passé composé. It is an auxiliary.

This division can be helpful to learn conjugations, especially the first group. The second group does not count many verbs. For the third group, there are different options: there are “model verbs”: learning one model helps us to conjugate the verbs with the same ending. For instance, when you learn the conjugation of tenir, you also know how to conjugate : appartenir, entretenir, retenir… There are also many irregular verbs in this group, and it may be a good idea not to learn them all, but only a few, the most useful ones, like aller or faire.