In French, there are several ways of expressing the past tense. Two of these are the Passé Composé and the Imperfect. To form the Passé Composé, conjugate your auxiliary verb (either avoir or être depending on which verb you want to put into the Passé Composé) and add the past participle of your verb. For example, if you want to say 'I have eaten,' you would take the 1st person singular form of avoir and add the past participle of the verb manger, leaving you with 'J'ai mangé.' To form the imperfect of regular verbs, go to the nous form of the present tense, take of the ending, and add the imperfect endings (-ais,-ais,-ait,-ions,-iez,-aient).
To differentiate between them, you need to know the context: if the verb is a completed action in the past (e.g. I gave her the book), you would use the Passé Composé (Je lui ai donné le livre). Also, if the verb happened in a specific timeframe (e.g. I was in France for five years), use the Passé Composé (J'ai été en France pendant cinq ans). However, if the action was a continuous action in the past (e.g. I was walking along the street), then use the imperfect (Je marchais le long de la rue). Also, if the action is repeated in the past (e.g. I saw my brother every day), use the imperfect (Je voyais mon frère tous les jours).