You first need to decide if you want to do this the quick and distressing way, or the slow and gentle way.
The quickest way would be to simply just bite the bullet. Spend time preparing and explaining in the daytime. At night into cot, fully awake after teeth brush and story. Kiss, say nan night and leave, closing door. Give it 5 or 10 mins (of screaming) and go back in. Quick kiss, say nan night and leave without faffing, closing door. Repeat repeat repeat.
It should be sorted within a week. Probably within 2 or 3 nights. But loads of lengthy screaming.
Other way is gently. It might take many months of gradually making changes. The idea is to take up stairs when slightly less of a deep sleep, very slowly and gradually as the weeks pass.
Say for example she starts going to sleep on sofa at 7.30 and is in a deep sleep and ready to take up at 8pm.
For a week or so take her up at 7.55, but stay in her room cuddling until 8.15 then into cot
Then have a week or so of 7.50 upstairs and in-room cuddle until 8.15 then into cot
Then upstairs at 7.50, in room cuddles until 8.10 and into cot at 8.10, but you stay with your hand on her chest/back until 8.30
Up at 7.45 for bedroom cuddles. Into cot at 8.00 for in-cot hand on chest/back reassurance until 8.30
Up for 7.30, into cot 8.00, leave 8.30
Up for 7.30, into cot 7.45, leave 8.15
Up for 7.30, into cot 7.45, leave 8.00
Up for 7.30, into cot 7.35, leave 8.00
... you get the idea