Oh dear! D:
Well here is how I do it:
Make sure you have 9 or more villagers,
Walk around town and see if anyone 'pings' (they should ping first thing)
if they don't, talk to the villagers you want to keep around 10 times, if someone is moving they will let you know, if not move onto the next day and repeat, you should get someone wanting to move within 4 days.
If the villager who is moving is one you want to keep, then tell them to stay. If they don't ping you so you can tell them then walk around for a while and see if that helps, if not move onto the next day and then they should ping you.
After you have got the villager to stay, TT 4 days into the future and start again.
I found that to improve the chances of the correct villager asking to move out you should talk to them twice, once for them to tell you they haven't seen you in a while and a second time for good measure, and then don't talk to them for a while.
Hope this all makes sense, any questions feel free to ask
