How do I connect my new tap's flexible hoses to my copper supply pipes?
I found some adapters which are designed for Flexi tap to quick connectors.

You simply screw one end on, then insert the other into the quick connectors like you would any other pipe.

Now that I've done it, it seems straight forward. But at the time i wasn't sure of the connection types or possibilities. Or how they worked.  

Really cheap and easy to do. Tool-less infact.