The subjunctive is used as a way to express doubt, possibility, or necessity of an action or situation happening. In a more broad sense it is used in sentences that are not assertions but rather express an uncertain or imagined action.
The sentence “I doubt that he is able to come”, for example, would be translated as “Je doute qu’il puisse venir”. Here the subjunctive present form of the verb “pouvoir” is used. When conjugating a verb in the subjunctive present, you would use the endings –e, -es, -e, -ions, -iez, -ent for each pronoun je, tu, il, nous, vous, ils respectively. The radical of subjunctive present verbs is often the same as the third person plural of the present tense conjugation for regular verbs (“pouvoir” is an exception). The verb “finir” for example, becomes “finiss-“ with the aforementioned endings added depending on the pronoun. The subjunctive is always used in a subordinate clause introduced by the prepositions “que” or “qui”.