There is this basic rule that the subjonctif is used after verbs, conjunctions and phrases of
1) hope
2) desire
3) fear
4) lament
5) admiration
6) doubt or
7) disapproval
Further, it is used when the main / introductory sentence implies that the subordinate clause is something irreal.
Examples
J' ai peur qu' il vienne.
I am afraid that he comes.
NOT: J' ai peur qu' il vient.
Je n' espère pas qu' il le fasse.
I do not hope that he will do it.
NOT: Je n' espère pas qu' il le fait.
Je crains qu' il soit déjà venu.
I am afraid that he is already there.
NOT: Je crains qu' il est déjà venu.
Before we now go into the details of the subjonctif, we should once more understand that the philosophy behind this mood of verbs is totally different from the English one, where in the past tense a conjunctive is used, but not in the present tense:
Example
I am afraid that he comes.
I was afraid that he would come.
Expressions with the verbs hope are used in English with the future; other expressions of hope and desire are used with the past conjunctive (= simple past):
Example
She hopes that they will be happy.
We wished that this was not true.
We will refer to these differences again, when going more into details with the subjonctif.