Hey chocobo_feathers!
There are two main ways of getting build/claim permissions:
1) When you claim an area of land using the golden shovel from /kit claim, you will automatically be given the build and claim permissions for that specific claim.
2) When a player trusts you on their claim using /trust IGN, you will be given the build and claim permissions for that specific claim.
These two methods will allow you to build on a certain claim; however, make sure that the area is claimed or else it may be griefed! Hopefully, that answers your questions. If you are still having problems, feel free to let us know.
Cheers!