Hi Basically when you rent a "Deeded Parcel" from someone on a private island, they "sell" you the parcel and you have full owner rights but you pay NO TIER at all to Linden labs and do NOT have to be a premium member. If you would like a small demo of this, you can IM me in world and Ill sell you a small parcel for 1 L$ so you can see what you can and do in most cases.
the process is you buy the land from a private island owner and that price goes toward rental fees you pay to the island Owner typically this is around 2000-2500 L$ per week for a 8192 parcel.
The owner of the island will typically have a tier rent box for you to pay each week, month or whatever. PLEASE READ THE COVENANT for the land before you buy. there may be rules or restrictions you may not like.