If you're doing the work yourself
Before you get rid of the waste, can any of it be reused? If you have things like old kitchen cabinets which are still in good condition, you might be able to give them away.
The easiest way to get rid of waste is to hire a skip. Check the hiring someone to collect your rubbish section for help on finding a legitimate company to dispose of your waste.
If someone else is doing the work
If you've hired a professional, like a builder, to do the work, they should take the waste away with them. It's important that you double check this before the project starts. Any costs for removing the rubbish should be included in the estimate they give you. If they're not, ask about it. You can also ask where your waste will be taken. Watch out for vague answers to this question - legitimate companies will know exactly what happens to their waste.