When do you use 'sein' and when do you use 'haben' in the past tense?

When forming a sentence in the past, or perfect tense in German, it is always formed with a conjugation of 'sein' or 'haben', plus the past participle of the main verb. It is much more common to use the verb 'haben' with the past participle, however many verbs take 'sein' instead. The verb 'sein' is used when:

1)There is motion/movement. E.g. gehen, fahren (to go, to go by transport)

"Wir SIND ins Fitnesszentrum gegangen"

2)When changing states. E.g. einschlafen (to fall asleep)

"Ich BIN eingeschlafen"

3)With the exceptional verbs bleiben and sein (to stay and to be)

"Sie SIND zu Hause geblieben"