Your landlord can't evict you unless he has has gone to court and proved that you did something wrong that justifies ending the tenancy.
And your landlord can't proceed with an eviction lawsuit without terminating the tenancy first. This usually means giving you adequate written notice, in a specified way and form. If you don't move after proper notice (or reform your ways -- for example, by paying the rent or finding a new home for the dog), the landlord can file a lawsuit to evict you. (This is sometimes called an unlawful detainer, or UD lawsuit.)
State laws set out very detailed requirements for landlords who want to end a tenancy. Each state has its own procedures as to how termination notices and eviction papers must be written and delivered ("served"). Landlords must follow state rules and procedures exactly.
If you do get hauled into court, and you can point to shoddy paperwork or the landlord's behavior, such as not maintaining the rental property in habitable condition, or retaliation for insisting on repairs, you can diminish the landlord's chances of victory.
Finally, even if the landlord wins the eviction lawsuit, she can't just move you and your things out onto the sidewalk. Typically, she must give the court judgment to a local law enforcement officer, along with a fee. The sheriff or marshal gives you a notice that the officer will be back within a few days to escort you off the property.
