I don't understand when to use the subjunctive and how to conjugate it?

In English, the subjunctive is used to express wishes or hypothetical situations, e.g. I wish you were nicer to me ('were' is in the subjunctive). In French, it's fairly similar. The subjunctive is associated with verbs that express desire, obligation, hope, doubt, uncertainty as well as for action that have not yet taken place. It is mostly used in the present or past tense and is constructed in such a way that it always has a que/qu' in front of the verb and its subject. For example: il est possible qu'il soit en retard ('soit' is in the subjunctive) - it is possible that he is late. 

Its conjugation is as follows: 

In the present tense : -e, -es, -e, -ions, -iez, -ent (verbs in -er, 1st group); -isse, -isses, -isse, -issions, -issiez, -issent (verbs in -ir, 2nd group); -e, -es, -e, -ions, -iez, -ent (other verbs, 3rd group) 

In the past tense: 'avoir' or 'etre' auxiliary + past participle 

Avoir auxiliary : j'ai, tu aies, il/elle/on ait, nous ayons, vous ayez, ils/elles aient 

Etre auxiliary : je sois, tu sois, il soit, nous soyons, vous soyez, ils/elles soient