The subjonctif présent is formed from the ils/elles form of the present tense: drop -ent and add -e, -es, -e, -ions, -iez, -ent. From ils parlent, you get que je parle, que tu parles, qu'il parle, que nous parlions, que vous parliez, qu'ils parlent — note that the nous and vous forms actually match the imparfait, not the present indicative.
Unlike the tenses covered so far, the subjunctive isn't really about time at all — it's a mood, used inside a subordinate clause (almost always introduced by que) to express something other than a plain fact: a wish, a doubt, an emotion, or a necessity. Il faut que tu partes (you have to leave) uses the subjunctive (partes) precisely because il faut que is one of the standard triggers for it.