File an eviction action. A landlord does not need to provide prior notice to evict a tenant for nonpayment of rent (unless this is subsidized housing; if it is, you are bound by the rules of subsidized housing), but may immediately bring an eviction (a/k/a "summary disposses") action. You would file in Special Civil court, in the tenancy or landlord-tenant division, and the court will serve the papers on your tenant.