Creating claims
To create a new claim, you'll need the Claim Tool. To obtain this, use /claimtool and a golden shovel will be added to your inventory. Warning: this command can only be used once, if you lose it, you'll need to craft a new Golden Shovel.
The claim tool tooltip, the username will reflect the user who used the command.

Selecting an area

Using the Claim Tool (Golden Shovel), select the opposite corners using left and right click. This will create an outline of particles. Make sure your points include the Y co-ordinate, as claims don't default to height limit.

Adjusting the selection

You can use/res select sizeto make the particles appear again to check your build is within the selection. To easily adjust your selection to make your build fit, you can use/res select shift[amount]while looking in the direction you want to expand(this works with y coords. too).

Creating the claim

Once you have your area selected, use /res create [name] and your claim will be created, with the cost charged from your on-hand balance.
A message will appear in your chat, confirming the creation, how much it cost, the area ID (more on this later), and the name you gave it. Residence names are unique, two residence cannot be named the same thing.