Not a lawyer, not legal advice, assuming you're in the UK, etc.
You automatically gain copyright protection when you create something original, no registration with any authority is required to give you this protection. Outside of the UK things get a little more complex. Theoretically legislation should protect you equally across the UK, the EU and the Commonwealth, but practically it helps if you take certain steps (displaying the copyright symbol/notice/date, registering with certain bodies, etc).
It all depends on what you're doing and where you'll be operating.
As for transferring it to clients, that's entirely up to you. You can include it in your service fees, charge them for it, or opt not to surrender it at all.