How is the perfect tense formed in German?

There are two different types of past tense in German - the perfect and the preterite. The perfect tense is more commonly used in speech and is arguably the easier of the two to construct. To construct the perfect tense in German, one needs what is called the 'auxilliary' form of either the verb 'sein' (to be) or the verb 'haben' (to have) and the past participle of the verb in question. The 'auxilliary' essentially means the forms of either of these verbs which correspond to the subject of the sentence or the person talking, so for example, the verb 'spielen' (to play) conjugates to 'ich spiele' (I play) but 'wir spielen' (we play), in the same way that the verb 'sein' (to be) conjugates to 'ich bin' (I am) or 'du bist' (you are). The 'bin' and 'bist' parts of these phrases are the auxilliary verb forms of 'sein', in the same way that the 'habe' from 'ich habe' would be the auxilliary verb form for 'haben' (to have).

Once one has correctly worked out the correct auxilliary verb form, the past participle of the verb itself is used to complete the perfect tense. In German, this is most commonly done by taking the stem of the verb's infinitive, dropping the -en at the end, replacing this with a 't' and adding 'ge' to the start, although there are multiple exceptions to this rule. For example, to put 'spielen' (to play) into the past tense, one must simply take off the ending and add a 't' and then add 'ge' to the front to form 'gespielt'. So, if one wants to say 'I have played', one must conjugate 'haben' to agree with the subject 'I' or 'Ich'. This would be 'habe'. Then one turns the infinitive verb 'spielen' into its past tense form 'gespielt' and combines the three elements - subject, auxilliary, past participle (S.A.P for short) to get 'ich habe gespielt'.