Be sure you give your landlord enough notice that you intend to move out.  If you have a month – to month rental agreement, you must give 30 days’ notice.  If you rent on a weekly basis, you must give at least 14 days notice.  Check your lease for any specific notice requirements including where to send the notice.

Use one of the forms of Notice to Landlord of Termination of Tenancy in the court’s Landlord/Tenant Act publication at https://public.courts.alaska.gov/web/forms/docs/pub-30.pdf.

Or you can just write a letter telling the landlord when you will move out and the address where you can be contacted after you move out.  Be sure you date the letter and keep a record of how you delivered it to the landlord.

No.  If you stay beyond the date you said you would move, the landlord may sue to evict you.  If you cause the landlord damages by overstaying, the landlord may also sue for 1-1/2 times actual damages. This could happen, for example, if the landlord has a new tenant waiting to move in, but the new tenant finds a different place to rent when you don’t move out, leaving the apartment unrented for another month or more.

If you have paid all rent when due, given adequate notice, and returned the apartment in a clean and undamaged condition, you are entitled to get your security deposit back.