It depends on a lot of factors. For example, the more furniture you have and the further you are moving, the longer you can expect the move itself to take. Typically, assuming the homeowners have prepared in advance, movers can pack up and load your furniture in one day or less.

A lot depends on your and your effort here. For moving day to go smoothly, you should take care of all of your packing responsibilities. This will enable the movers to come in and take care of their part of your move as quickly and efficiently as possible. Once the movers arrive at your home, they will have a much easier time loading your furniture and other items if you have taken care of all of your responsibilities.

To my mind If you are just moving across town, it is entirely possible that your movers will be able to completely finish moving your furniture out of your old home and in to your new one on the same day. This is possible only if things go smoothly and you don't have a very large quantity of furniture and other belongings.

If you are able to get moved into your new home on the same day you leave the old one, you will save money on your moving expenses and be happy that the stress of your move is behind you.