I am in the same situation; I rent out the downstairs apartment in my two-family rowhouse. Read up on landlording in general, because almost all of the advice will apply equally to this situation. But here are a couple of considerations that are unique to this situation:
- like CowboyandIndian said, your tenant will also be your downstairs neighbor, so you will want to scrutinize prospective tenants wearing both your landlord hat and your upstairs neighbor hat (luckily, your interests in both of these capacities are largely aligned). But when selecting tenants, make sure you do not discriminate against applicants in any way that is illegal--research applicable law in your location, because it is not always self-evident which criteria are illegal to use in the selection of tenants.
- because you and your tenant will be next-door neighbors, it may be harder to maintain an arms-length business relationship. Be a friendly and respectful neighbor and a friendly and respectful landlord, but try not to let either relationship compromise the other.
- on your point about the utilities, you should find out how much it would cost to have them separately metered and run the numbers to see if it's worth doing. In any event, if you will be covering the utilities and that is not normal for a rental in your area, you should factor that into the rent you charge.