It's quite simple ... it's only a notice in writing, but are you the tenant or landlord? For tenants, it could be something along these lines:
To: (Name of landlord)
As of (date of move), I will be vacating the dwelling at (address). It is understood that any monies owing to you have been paid in full (especially if you paid first and last rent, or a security deposit).
If you're the landlord:
To: (Name of tenant)
This is notification that you must vacate the dwelling at (address) no later than (date). Any monies owed to me must be paid by this date to avoid legal proceedings.
It is like writing a normal letter. You have to state your intention to vacate and probably provide reason why are you vacating the apartment.