Use the verb evict to say that a tenant is being forced to move out of his home, usually through legal action. If you don't pay your rent, eventually your landlord will evict you.
Evict became part of the English language back in the 1530s. Based on the Latin word evincere, meaning "recover property, overcome and expel, conquer," even then it had a legal process attached to it. Before you evict someone, you have to complete official paperwork, though some landlords may succeed in evicting tenants without following the legal steps.