I had carers when I had no hip. At first Social Services instructed a local care agency to send carers out, but then they offered me Self-Directed Support which I trialled using the same Agency with a view to moving on to Direct Payments.
Social Services allocate a budget based on the number of hours care needed, then you can either hold the money in a separate account yourself and advertise for a carer(s), employ them yourself, do their wages etc. etc., or employ an agency to send out staff. In my area, there is an organisation who will do the wages for you and offer support, i.e. employment disputes etc., for a weekly fee of about £6.50. I believe public liability insurance is paid by Social Services/County Council. The guy that came out to see me about doing wages etc. suggested firing the carer before you've employed them for a year, so as to avoid them gaining too many employment rights, i.e. redundancy.
In theory, it sounded good, but as others have said, its difficult to find a carer that does the job properly. Mine was ok but often didn't stay the allocated 45 or 30 minutes, didn't want to do any housework, which they were told to do under SDS, turned up an hour late and basically weren't worth the hassle. Communication between Agency and staff was non-existent. If I cancelled them, they would turn up anyway and no-one ever knew what was going on. In the end I told them I would try on my own and I'm now glad to be rid of them.
The place to find out more would be your County Council website as each County does things slightly differently.
Carol