The subjunctive is one of the most important new aspects of Spanish grammar learnt at A Level. It is actually far more simple than people make it out to be, and Spanish speakers use it all the time! It isn't called a tense but a mood, meaning you can use the subjunctive in the present and the past tense. It is used when there is some quality of uncertainty or subjectivity, as opposed to something that is a fact or that you are sure of. For example, you would use it in the sentence "Dudo que vaya a Madrid en diciembre", because there is doubt and uncertainty - but you wouldn't use it in the sentence "No dudo que va a Madrid" because you feel certain of it. To learn all the uses of the subjunctive in Spanish, I always remember the acronym WEIRDO (which stands for wish, emotion, impersonal expressions, requests, doubt, and ojalá). This helps me remember when I should use the subjunctive when writing my essays.
The conjugation of the present subjunctive is fairly simple. You conjugate -ar verbs as if they were -ir or -er verbs (e.g. "yo hable") and vice versa (e.g. "yo exista"). However, naturally there are several crucial irregular verbs that need to be learnt by heart, such as ir, ser and tener. It's important to remember that the negative imperative uses the subjunctive as well (e.g. "¡no me digas!").