How do I form the passé composé and when do I use it?

When do I use the passé composé? 
The passé composé is used to describe a completed past action. If you imagine that you were looking at your watch for the duration of the action, and could therefore give a precise time for the start and end of the event, the passé composé is the appropriate tense to use. 

Some examples in English:

• He entered the office at 2pm.
  
• Yesterday, they went to the cinema together. 

How to form the passé composé:
You will need to know... 
1. The French Subject Pronouns: Je (I), Tu (you - singular), Il/Elle/On (he/she/one), Nous (we), Vous (you - plural/formal singular), Ils/Elles (they)
2. The auxiliary verbs avoir and être in the present tense: j'ai, tu as, il/elle/on a, nous avons, vous avez, ils/elles ont ; je suis, tu es, il/elle/on est, nous sommes, vous êtes, ils/elles sont. 
3. How to form the past participle of the verb in question and which auxiliary it requires:

• Regular ER verbs: remove 'er' from the infinitive (this is the "to" form of the verb that is found in the dictionary) and add 'é'. For example, 'manger' (to eat) becomes 'mangé'.
  
• Regular IR verbs: remove 'ir' from the infinitive and add 'i'. For example, 'choisir' (to choose) becomes 'choisi'.
  
• Regular RE verbs: remove 're' from the infinitive and add 'u'. For example, 'vendre' (to sell) becomes 'vendu.' 
  
• Unfortunately, there are many irregular verbs that need to be learned. You can find lists of the most common irregulars online, for example here: http://www.bbc.co.uk/schools/gcsebitesize/french/grammar/verbsf/perftenseavoirrev2.shtml
  4. The fact that verbs taking être can be remembered using the acrostic 'DR MRS VAN DER TRAMP.'
  Devenir - Devenu - became
  Revenir - Revenu - came back
  Monter - Monté - went up
  Rester - Resté - stayed
  Sortir - Sorti - went out
  Venir - Venu - came
  Aller - Allé - went
  Naitre - Né - was born
  Descendre - Descendu - went down
  Entrer - Entré - entered
  Rentrer - Rentré - went back in
  Tomber - Tombé - fell
  Retourner - Retourné - returned
  Arriver - Arrivé - arrived
  Mourir - Mort - died
  Partir - Parti - left
  5. The fact that verbs taking être must agree in quantity and gender with the subject. 
  
• add 'e' to the past participle for feminine singular. 
  
• add 's' to the past participle for masculine plural. 
  
• add 'es' to the past participle for feminine plural. 

Examples of the passé composé:

• Ils sont allés au cinéma ensemble. 
  
• Elle est née hier.