How do I form the subjunctive mood? And what is it for?

First of all, it is necessary to recognise that the subjunctive is not a tense, but rather a mood. This means that it is used to express certain moods and emotions through the verb, rather than a period of time (tense). The emotions expressed can be remembered through the acronym DEW - doubt, emotion and wish. An example of doubt - 'no pienso que sepa lo que está pasando' (I don't think she knows what's happening). Note that the verb 'saber' (to know) is irregular in the subjunctive - I will write a table of irregulars.
In Spanish, the regular present subjunctive is formed by reversing the verb endings for the verbs. Take 'hablar', an -AR ending verb, which, conjugated in the 3rd person singular is 'habla' (he/she/it speaks). In the subjunctive, this ending 'a' is replaced by 'e', the regular ending for -ER/-IR verbs, so the verb becomes 'hable'. This goes for regular -IR/-ER verbs too - 'recibir' in the 3rd person singular is 'recibe', however, in the subjunctive, this becomes 'reciba' (an -AR verb ending). See how the endings have been reversed? I will write a table with the regular conjugations as a guideline.