You should use the subjunctive in a few cases, which are all dictated by grammatical structure. Usually, the subjunctive indicates a 'feeling' in the verb, especially of fear, doubt, or uncertainty. It is never in the main clause of a sentence and is almost always introduced by que.
1. After certain set expressions
The subjunctive must be used after certain expressions. These have to be wrote learnt. Some of them are very common (pour que, avant que, afin que, quoique):
Quoique vous ne soyez pas prêts, faites ce que je demande. - Although you are not ready, do as I ask.
Je lui ai demandé de m'aider, pour que je puisse finir plus tôt. - I asked him to help me, so that I could finish sooner.
2. After certain verbs
Certain verbs + que must be followed by the subjunctive. Especially important are:
verbs of wishing (désirer que, préferer que)
verbs of fear (craindre que, avoir peur que)
verbs of ordering, permitting or forbidding (demander que, permettre que)
verbs of emotion (avoir honte que, s'étonner que)
3. After superlatives
When we use a superlative to describe something (le plus grand, le meilleur, le pire etc.), a following verb must be in the subjunctive:
C'est le plus grand homme que je connaisse. - He's the biggest man I know.
C'était le pire film que j'aie jamais vu. - It was the worst film I've ever seen.
4. After negative forms of some verbs 'of thought'
Some verbs which do not need the subjunctive normally do when they are negative. Almost all are verbs to do with thinking or opinions. One of the most important is penser que.
Je pense qu'il est fort. - I think that he is strong.
Je ne pense pas qu'il soit fort. - I do not think that he is strong.
5. In certain set expressions
Some set expressions require the subjunctive, and these have to be learnt by heart.
Vive la reine ! - Long live the Queen!
Que Dieu vous bénisse ! - God bless you!
6. When an object or person may not exist ('indefinite antecedents')
When an object or person may or may not exist, we can use the subjunctive to indicate this doubt or uncertainty:
Je cherche quelqu'un qui sache parler français. - I am looking for someone who speaks French. (They may not exist).
Je cherche quelqu'un qui sait parler français. - I am looking for someone who speaks French. (I know they exist).