Le Passé Composé is mostly used where English uses Simple Past

Look at these usages of Passé composé:

Je suis arrivé à 18h30.I got there at 6.30pm.

L'Angleterre a gagné la bataille de Trafalgar en 1805.England won the battle of Trafalgar in 1805.

J'ai acheté un pull ce matin.I bought a jumper this morning.

Il a préparé le dîner, il a mis la table, puis il a attendu qu'elle rentre du travail.He made dinner, set the table, then waited for her to come home from work.

Note that although Passé composé is structurally similar to English Present Perfect (I have done), in most cases, it is the direct equivalent to the English Simple Past (I did).
Indeed, the French Passé composé refers to a single past action that is definite, with a clear start and end, and looked at as one point in time (hence often paired with a clear date or timeframe). 

ATTENTION:

In some cases, Passé composé can be translated either as Simple Past or Present Perfect:
J'y suis allé deux fois aujourd'hui. I went there twice today.

J'y suis allé deux fois aujourd'hui.I have gone there twice today.

The nuances we have in English between I went and I have gone don't really exist in French. They're instead expressed through the context and the tone used.

 

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Examples and resources

J'ai été impressionnée par sa présentation.I was impressed by his presentation.
J'y suis allé deux fois aujourd'hui.I have gone there twice today.
Je suis arrivé à 18h30.I got there at 6.30pm.
J'y suis allé deux fois aujourd'hui. I went there twice today.
L'Angleterre a gagné la bataille de Trafalgar en 1805.England won the battle of Trafalgar in 1805.
Il a préparé le dîner, il a mis la table, puis il a attendu qu'elle rentre du travail.He made dinner, set the table, then waited for her to come home from work.
Tu as fini ton travail avant 10 heures.You finished your work before 10.
Lundi dernier, Lucas et Tom ont joué au foot.Last Monday, Lucas and Tom played football [US: soccer].

generally


J'ai acheté un pull ce matin.I bought a jumper this morning.
Let me take a look at that...