Your landlord accepts credit card payments and you pay him/her with your credit card? No different than any other vendor. Mine charges like 2% or something to cover costs.
My last landlord waived the fee if we had it set on automatic bill pay (via the credit card), I'm not sure if the peace of mind was worth the loss, but considering rent was 750 dollars, 2% would have only been 15 dollars. They probably pad the rent a bit to make up for it, but 750 for a 2 bedroom apartment was still a pretty good deal for the area at the time.
What I meant to ask was, "How do you pay rent with credit (without paying $30-40 each month for the privilege)?"