In French, like in most European languages, verbs must be conjugated to agree with their subject and to express the time of the action or the state of affairs referred to in the sentence. This is usually done by keeping the stem of the verb, which can vary, and attaching an ending to it.
In French, conjugations can be of two kinds: simple or compound. The first one is called "simple form" because it only consists of the verb conjugated (stem + correct ending). The second one is called "compound form" because the auxiliary verbs être and avoir are used to build them. In compound conjugations, only the auxiliary verbs are conjugated, whereas the form of the verb is always the past participle. All French verbs use either être or avoir in compound tenses, but some verbs can use both, in which case the meaning is different:
e.g.: je suis sorti. I went out. But j'ai sorti les poubelles. I threw the rubbish out.
e.g.: je suis monté à l'étage. I went upstairs. But j'ai monté le café à l'étage. I brought the coffee upstairs.
It is common to say that action verbs usually require avoir whereas state verbs and verbs of movement require être. If conjugated with être, note that the past participle must agree with the subject. With avoir, the past participle does not agree with the subject, but it does agree with the direct object when the latter comes before avoir. Pronominal verbs always use être.
French verbs are usually categorized in four moods: indicative, imperative, conditional and subjonctive.
"Infinitive" is the name given to the dictionary form of the verb (when it is not conjugated). You can easily recognize the infinitive form of French verbs : the endings are always -er, -ir or -re.