Firstly, do not worry! Even in my second year of university I'm still not 100% confident about using the subjunctive. A lot of it is simply instinctive and only becomes obvious after years of exposure to the language. Having said that, there are a few rules that you must learn.
The most important thing to remember is that the subjunctive is not a tense, but a mood. It is used to express a wish, hope**, fear, uncertainty***, and other attitudes or feelings toward a fact or an idea.*
Often, there is a subject and an object involved. The subject wishes/hopes/doubts/fears/wants the object to carry out an action.
e.g. Je veux que tu fasses la vaisselle.
In this sentence the subject is 'je' and the object is 'tu'.
If there were only one person involved, the infinitive would be used i.e. 'je veux faire la vaisselle' or 'tu veux faire la vaisselle'. You would NEVER say 'je veux que je fasse la vaisselle'. It sounds silly!
Other examples
Il doute qu'elle vienne.
On a peur qu'ils aient eu un accident.
Le livre recommande qu'on fasse beaucoup d'exercise.
Je ne veux pas que vous mangiez mon gateau.
The subject may express general feelings about the object's actions, in which case the subjunctive is used.
E.g.:
Je suis contente que tu sois la.
Il me rend triste que certains enfants n'aient pas de parents.
Finally, some phrases just trigger the subjunctive. Whenever you hear the phrase, the subjunctive must always come after - no exceptions. This includes:
avant que****
il faut que,
il vaut mieux que,
il est important que,
il est dommage que
Pour que
afin que,
de sorte que,
de crainte que,
de peur que,
avant que,
en attendant que,
jusqu’à ce que,
bien que,
à moins que,
à condition que,
pourvu que
je ne pense pas que
With enough practice, you'll get a natural feel for it, especially since all the phrases end with 'que'. Try to get into the habit of asking yourself whether you need the subjunctive every time you use this word.
*Any verb that is not in subjunctive form is in the indicative.
**However, esperer (to hope) does not take the subjunctive as would be expected. We use the indicative future e.g. 'j'espere que tu reviendras'
***'Il est probable que' always takes the indicative future because although whatever it is is not completely certain, it is more certain than uncertain (confusing, I know!) e.g. Il est probable qu'il pleura.
****This is because the action has not happened yet and is still not definite e.g. 'avant qu'il soit parti'. However, 'apres que' takes the indicative because the action has already definitely happened: 'apres qu'il est parti'.