I have addressed this topic in previous threads and comments (here, here, and here, for example), both on this blog and on various forums, but it looks like when you need the answer, it can be hard to dig out. So I'm hoping that by placing these steps in a dedicated post, they will become easier to find.

When you restore a database that uses encryption features, there is only one thing you need to take care off - if the database master key (DbMK) needs a service master key (SMK) encryption, you need to regenerate this encryption. Note that this encryption is made by default when you create the DbMK, but it may be intentionally dropped, if you want tighter control of access to the encrypted data. Anyway, if you did have such SMK encryption for the DbMK, the steps to regenerate it are the following:

OPEN MASTER KEY DECRYPTION BY PASSWORD = 'password'
ALTER MASTER KEY ADD ENCRYPTION BY SERVICE MASTER KEY
CLOSE MASTER KEY

That's it - the database encryption features should now work as when the backup was taken. Also note that it doesn't matter if you restore the database on the server where the backup was taken or elsewhere. The only thing that matters for this procedure is that you know one of the passwords protecting the DbMK (yes, there can be more than one - see this post).