Spanish Conjugation help!?

ok. so for the present tense I have the sentence. I stretch after I wake up. I conjugated it as me estiro despues me despirtar. What i'm confused on is wether I conjugate the 2nd work ( despertar). Btw, despertar has a ie change such are, me despierto. Please help me and tell me wether the 2nd word needs to always be conjugates or not. Thank you.