The subjunctive is one of 3 moods in German (indicative, imperative, subjunctive). Every verb in every sentence falls into one of these three categories. The most common (by far!) is the indicative mood.
The subjunctive 1 is used for indirect speech and indicated by conjugating the verb in a specific way.
The most common place to find it is in the news (newspapers, on TV, etc.) and in fixed expressions.
The teacher says: "Deutsch ist nicht schwer!"
The student says to his friend: "Mein Lehrer sagt, Deutsch sei nicht schwer."
⇒ The quote was said by the teacher, and the student is saying what the teacher said.
In English, we conjugate verbs like normal when indirect speech is involved and just add in that someone else said this. In German, however, the verb is conjugated differently to really show that this is the opinion / belief of someone else.
Theoretically all verbs and persons (i.e. first person singular, second person plural) have a subjunctive 1 form, but in practice "sein" is the only verb where all persons are used:
For all other verbs the subjunctive 1 is normally only used in third person singular (er/sie/es/man):
To form the subjunctive 1 for third person plural, you just take the "-n" from the infinitive form:
In second person (du/ihr) the subjunctive 1 is used rarely, and all that you have to do is add an "e" before the ending:
In informal language, the subjunctitve 2 would be used.
In first person singular and first / third person plural, the subjunctive 1 is not used. Instead, use the subjunctive 2 or the normal indicative form.
Er sagt: „Wir gehen ins Kino.“
The subjunctive 1 can be used in the simple present, perfect, and future tenses.
The conjugated verb is put in the subjunctive I form.
The subjunctive is also used in specific fixed expressions:
In informal speech we don‘t really use the subjunctive 1.
Instead, we use the indicative and a clause containing "dass":
This sentence is only 100% grammatically correct with the subjunctive 1. However, only German teachers and linguists would notice it.
It's important that you understand the tense, but most German learners don't need to spend so much time mastering it. It's only critical in a few specific areas like law and medicine.