Game guide: Asking Sims to move in
The Sims 3
In The Sims 3, two Sims must have a relationship of friend or higher for one to ask the other to move in. Have the Sim you want to ask perform friendly socials until "[Friend] thinks [Sim] is being friendly" appears. The target can then be asked to move in. Note that if the target has the Commitment Issues trait, it will take longer to be able to invite them. Also, if the target is a single parent, their children must be moved in as well.
To move a Sim in without hassle, use "testingcheatsenabled true". If Late Night is installed, right-click on the Sim and choose "Add To Active Family". Otherwise, drag the relationship bar to full and do friendly socials until the "[Friend] thinks [Sim] is being friendly" message pops up, then ask the Sim to move in.
Also, if the Sim lives in a household, he/she can be moved out and moved into the desired household.