When you place your first chest, you'll get an automatic land claim around the chest. You'll see glowstone and gold blocks on the ground, outlining your claimed area (those blocks are inside your claim). Those blocks are only markers (you can't collect them), and only you can see them. Place other valuable blocks like more chests, your furnace, and your bed within the protected area to keep them safe. To see the markers again later, you can use a piece of string (right-click).
When you get a golden shovel, you can expand your claim or create additional claims (see the video above). Use /AbandonClaim to delete a claim you own, or /AbandonAllClaims to delete all your claims at once.
The simple claim sharing command is /Trust, which gives another player permission to build in your claim. /AccessTrust grants access to ONLY buttons and switches, while /ContainerTrust permits a player to access your claim and additionally open your containers (chests, etc) and use your crafting equipment. Use /UnTrust to revoke any granted permissions, and /TrustList to see who has permission.
You can permit another player to share his permission level with others by using /PermissionTrust. That player can't resize or delete your claim or use /PermissiontTrust on your behalf, but you should use this command sparingly because you may soon find that many strangers can access your claim. To clear away all permissions for all players in your claim, use /UnTrust all.
You'll get claim blocks over time just for playing, as long as you're not idling (just standing around and chatting). As long as you appear to be actively playing the game, you'll continue to get claim blocks. If it's allowed on your server, you can also buy claim blocks with /BuyClaimBlocks and sell them with /SellClaimBlocks.
For you advanced users out there, claims may be subdivided so that you may manage permissions for different areas of your claim (think workshops, fields, and residential plots) separately. To get started, use /SubdivideClaims. You may resize subdivisions just like you resize your top level claim, and can delete a subdivision by standing inside it and using /AbandonClaim. To "evict" a tenant and all the friends he may have shared permissions with, use /UnTrust all.
Player Command Reference
(See administrative details page for admin commands and permissions.)
Deletes the claim you're standing in.
Gives another player permission to edit in your claim.
Revokes any permissions granted to a player in your claim.
Gives a player permission to use your buttons, levers, and beds.
Gives a player permission to use your buttons, levers, beds, crafting gear, containers, and animals.
Lists the permissions for the claim you're standing in.
Switches your shovel to subdivision mode, so you can subdivide your claims.
Puts your shovel back in basic claims mode.
Grants a player permission to share his permission level with others.
Removes all permissions for all players in your claim.