Monica found Phoebe through a roommate-matching service and she moved in.
I 'googled" it..here is part of the article....
2.06 How did they all meet? (Friends)
JG: "O.K., here's the quasi-definitive answer as I know it, as we writer folk have discussed it over the course of the season...
"In the pilot, we established that Monica, Rachel and Ross all went to lincoln High School together. Monica was fat; Rachel was popular and possibly bitchy; Ross was a nerd. Rachel says that she and Monica were close, but in the time since, they've drifted -- enough so that Rachel didn't think to invite Monica to her wedding.
"We also established that Ross had a crush on Rachel back then; she knew this, but thought of him as 'Monica's geeky older brother.'
"During the making of 'The One Where Nana Dies Twice' , Schwimmer and Perry wondered if Chandler and Ross might have gone to college together. We writers agreed that it might be nice for two of our other characters to have a history together, so we wrote it in.
"Therefore, my guess is that when Monica graduated college and was looking for an apartment, Chandler (who was living with his first roommate Kip -- the one Joey is jealous of in 'Dozen Lasagnas' ) alerted her to the fact that an apartment was opening up across the hall from him. Monica found Phoebe through a roommate-matching service and moved in.
"One of the ways we've justified -- to ourselves, at least -- this amazing place Monica lives in (on an assistant chef's salary!) is that it's probably an illegal sublet. Several plot lines revolving around this fact were discussed over the course of the season, but never amounted to anything."
(Alexa later added: "Rachel and Monica live in a rent-controlled apartment Monica's grandmother left her (not Nana - the other one) This information was actually in an episode, but cut out for time.")
JG: "Anywaaaaaay... When Kip got married, he moved out and Joey (who Chandler probably also met through a roommate-matching service, atau by putting up flyers at the laundromat) moved in. Around the same time, Phoebe's grandmother needed some kind of taking care of, so Phoebe moved out of Monica's to live with her. This is another element we talked about a lot over the course of the season, but it never found its way into a story.
"As for the timing of the events surrounding Ross's divorce, that's something we've consciously avoided getting into. The lebih anda think about it, the lebih troublesome it becomes: Was Carol already involved with Susan when Ross got her pregnant? We invite viewers to figure this one out for themselves..."
monica n phoebe were roommates at first. remember they had da episode when phoebe was moving out little sejak litte n monica says dont send the lamp to the same place u took the radio they had that for weeks!
monica and phoebe used to be roommates but phoebe moved out without telling monica because she went to live with her grandmother but she couldnt tell monica because she didnt want her to be upset but at the begining they aint roommates so we see this in one of the flashback episodes :)