The perfect tense is one of three German past tense forms. It's also the one that's most commonly used in spoken German, so very useful to learn. The perfect tense is a compound tense. This means it uses two verbs: an auxiliary (or helper) verb and a main verb. Most of the time, the auxiliary verb is haben, which means to have. But for some verbs, especially intransitive verbs of motion and intransitive change-of-state verbs, the auxiliary verb is sein, which means to be. The main verb then shoots along to the end of the clause and appears in the form of a past participle. As a rule of thumb, you create the past participle of a verb from its infinitive by adding a ge- on the beginning, and sometimes you switch the or the on the end for a . Two examples of how you make a perfect tense sentence are:

Ich habe ein Eis gegessen - I have eaten an ice cream
Ich bin in die Schule gegangen - I've gone to school

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While I was researching this podcast, I found a couple of particularly useful websites. Here are the English ones:

A description of when to use the different German past tenses:
http://german.about.com/library/verbs/blverb_past.htm

A description of how to use the German perfect tense:
http://en.wikibooks.org/wiki/German_Grammar:Verbs:Past_Tenses:Perfect_Tense

Exercises (particularly suitable for beginners) to practise using the perfect tense:
http://atschool.eduweb.co.uk/rgshiwyc/school/curric/German/Revision/German_Perfect_Tense/index.htm

And here are the German ones (two descriptions of when Germans say you should use the perfect tense and when the simple past (also known as the imperfect tense or the preterite)):

http://de.wikipedia.org/wiki/Pr%C3%A4teritum
http://home.schule.at/cometo/latein-griechisch/grammatikmerkblaetter/perfektimperfektverwendung.htm