I don't know Touhou that well, but here are the transformations:
Marisa is doing some testing or experiment with the guy to start. She then uses the staff on the guy which makes him look like herself on accident. She doesn't know how to reverse the affect, so she is going to Patchouli's mansion to consult her. She then ties up the "Marisa" guy so he can't fool around with the body.
Patchouli explains its a magic item that makes the other person look like your real self. She uses it on Marisa and makes her look like Patchouli. She then hands the staff to Marisa and has her use it, which makes Patchouli look like Marisa. Marisa then says they should change clothes -- so after swapping clothes, you have Marisa as Patchouli in body and clothes, and vice-versa. Patchouli's maid comes by with business for her, and not recognizing they had switched, walks off with Marisa -- she goes with the flow and leaves Patchouli to deal with the problem instead.
Alice came visiting and found "Marisa" tied up -- part after that is pretty self-explanatory. Then Patchouli as Marisa comes in and Alice says "if thats Marisa, then whose the Marisa in the chair?" -- so she then uses the magic item on the guy and changes him into Patchouli and says "I'm surprised at you Alice, I never knew you liked Patchouli" while imitating the tomboy mannerisms Marisa uses.
After that she proclaims her love for "Patchouli" and the rest you can figure out. End is Marisa as Patchouli in the library saying "reading books sure is fun" basically.
(I think earlier after Patchouli had Marisas body she was feeling it up and probably thought something about liking Marisa. So thats probably why she went for the "proxy sex" later on...)
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