Many languages express the past with a single verb form — you conjugate one word and you're done. Spoken everyday German works differently: outside of a handful of verbs like sein, haben, and the modal verbs, everyday speech barely uses the simple past (Präteritum) at all. Instead it builds the past tense out of two verbs working together: a conjugated helper verb (here, haben) that agrees with the subject, plus a fixed, unchanging form of the main verb called the Partizip II, which always sits at the very end of the sentence. This two-part construction is called the Perfekt, and it's the first past tense you use to talk about finished events.
Why two verbs instead of one? Because the Partizip II never changes according to the subject — gemacht stays gemacht whether you say ich habe gemacht or wir haben gemacht. The helper verb alone carries the information about who is doing the action; the Partizip II only carries the meaning of the verb itself. Most German verbs (roughly 80%) use haben as their helper, including every transitive verb (one with a direct object) and every reflexive verb.
How to build it step by step: first, conjugate haben to match the subject (ich habe / du hast / er hat...) and place it in second position, the normal verb slot in a statement. Second, form the Partizip II: the regular pattern is ge- + stem + -t (machen → gemacht), but many common verbs are irregular and simply have to be memorized one by one (essen → gegessen, trinken → getrunken). Third, push the Partizip II all the way to the end of the sentence, no matter how much material — adverbs, objects — comes in between. In questions, haben moves to the front and the Partizip II still stays at the end: Hast du das gemacht?
Watch out for separable verbs like aufräumen: the prefix auf splits off, and ge- is inserted between the prefix and the stem, not before it — giving aufgeräumt, not geaufräumt.
A very common mistake is putting the Partizip II right after the subject, following the word order of one's native language, producing the wrong Ich habe gemacht meine Hausaufgaben instead of the correct Ich habe meine Hausaufgaben gemacht. Keep the golden rule in mind: the Partizip II always goes to the very end, no exceptions.