Pesky tenants who don't pay their rent or who don't treat the landlord's property with anything resembling respect are not as easily gotten rid of as calling the exterminator to eliminate six-legged creatures. In most states, the landlord first has to send the undesirable tenant a formal letter of notification that spells out what the problem is -- whether the tenant is behind in paying the rent or whether he's otherwise violating the terms of the lease (destroying property or making too much noise, etc.). The tenant is given the choice of shaping up or shipping out, or eviction proceedings will be started.
The landlord and tenant appear before a judge with any evidence that they have to support their claims. The judge then determines if the landlord is justified in his complaints, and if so, the landlord is given a writ of possession, which states that the tenant has to move out within a certain number of days. If he doesn't move out, the landlord can get a sheriff or marshal to evict him. The landlord can't kick the tenant out himself or turn off the electricity or water. If the tenant doesn't take his possessions with him, depending on which state he lives in, the landlord might have to hang on to the possessions for a few days before throwing them out, giving them away or selling them.
If the judge determines that the landlord is behaving like a slumlord, trying to evict the tenant in the middle of the lease so he can raise the rent, or otherwise isn't in the right, the tenant wins the case, the landlord has to pay the legal fees and the tenant can remain in the apartment.