To start off with any claim, admin claim, etc... You need a golden shovel. Just a normal golden shovel.

Every block you get you can claim 1 block with your claims, (Ignored by Admin Claims) In the default config you start with 100 claims blocks to start with a small claim. Every hour you get 100 claim blocks, again in the default claim you can only have 80,000 claim blocks stored up constantly.

Basic Claiming Mode - /bc (Default Mode)
Ignoring the fact that you have a set amount of claim blocks you can right click in a selection like WorldEdit (Click on 2 corners) and it will create a claim. This claim expands from Y 256 to Y 0 so you can just add 1 layer of claim blocks.

Admin Claiming Mode - /ac (Admin Mode)
Admin Mode ignores all your claim blocks so pretty much you have infinite, admin claims are claims that admins can access but no one else, it unlocks some things like button pressing and stuff like that instead of a normal claim where those are blocked. (USEFUL FOR SPAWNS)

Deleting your own claims as a player all you have to do is do /abandonclaim or /unclaim while you are standing in your claim. To remove ALL your claims you do /abandonallclaims

GriefPrevention makes adding people to claims very easy. To give people access to a certain claim do one of these three commands while in that claim
/trust (Gives them full access) - Level 3 Perms
/containertrust (Beds, levers, containers, etc...) - Level 2 Perms
/accesstrust (Beds, levers, buttons) - Level 1 Perms
To untrust someone do:
/untrust in the claim
Or to give someone access to ALL your claims stand in the wild where there are no claims and do one of those three commands

Admins have commands to give people different amount of claim blocks.
/acb {player} {amount} (Adds claim blocks to players claim block amount) - Can go over limit of 80k default
/scb {player} {amount} (Sets claim blocks of players claim block amount) - Can go over limit of 80k default