When I've needed a furnished apartment, I've done it separately -- rented an apartment, then rented furniture separately. They'll come in and set up the furniture and come and pick it up when you move out.

Last time I rented furniture, it cost around $250/month to furnish a one bedroom apartment. They supplied all of the furniture, we supplied dishes and cookware.

For a longer term lease, it may be cheaper to buy cheap furniture from Ikea, but it's a lot more hassle, it's so much easier to let the rental company come in and set up, then take it all away when you leave.