1. A tenant can exclude everyone else from the rental property, including the landlord. Most leases, however, modify this right by specifying that the landlord has the right to enter for certain purposes (i) at any time (she smells smoke coming from the premises, for example) or (ii) upon advance notice (a 24-hour advance notice for a routine inspection of her proerty, for example). Applicable law also requires the tenant to allow entry to certain third parties such as a fire code inspector or a policeman with a warrant. If Ted Tenant signs a lease and Laura Landlord fails to move out the previous tenant on time (or lives there herself), then Ted can sue to have the previous tenant or even Laura forcibly ejected.
A word of warning, however - if the previous tenant refused to leave and produces a valid lease whose term hasn't ended by the time Ted's term began, then Ted cannot evict the old tenant - he'll have to terminate his lease and sue Laura for damages. The amount of the damages will probably be equal to the expenses of seeking new premises plus any amount by which Ted's new rent exceeds the rent he would have paid to Laura (assuming roughly equal accommodations).
2. Suppose the previous tenant's lease expired but he refuses to move out - what can Ted do? Well, that depends on whether the old tenant is still willing to pay rent. If he isn't, then Ted will have to sue to eject the old tenant, but will still have to pay rent to Laura even before the old tenant is ejected - and he'll have to sue the old tenant to get back the rent he paid to Laura, because he cannot sue Laura for it (Laura can also sue the old tenant for ejectment and rent, but she cannot collect rent from both Ted and the old tenant for the same month).
On the other hand, if the old tenant IS willing to continue paying Laura rent even though his lease has expired, then what Ted can do depends on how Laura responds to the old tenant's offer to continue paying rent. If she refuses the offer, then refer to the last paragraph for Ted's options. But if she accepts the rent from the old tenant, then she is violating Ted's lease by refusing to hand over possession of the premises. Ted can either (i) terminate the lease and sue Laura for whatever damages he has sustained(as in paragrpah 2 of item 1 above), or (ii) sue the old tenant for ejectment and damages (but he will not owe Laura any rent for the time the old tenant overstays). If he chooses option (ii) he can also sue Laura for any damages he may have sustained for the inconvenience, but will still have to pay rent from the time the old tenant moves out until the end of the lease term.
Keep in mind that US landlord-tenant law varies from state to state, and is subject to intereptation (which is why lawyers make so much money!)
DISCLAIMER: The following is intended for reference purposes only and not as legal advice.