Hey Lucy P...
I think I have addressed this situation with my faucet: the copper tubing was a solid piece, soldered directly to the faucet.
There are a couple ways to do this but the easiest is to use a compression fitting (vs sweating on new fittings).
To use a compression fitting, you'll need to cut the existing copper tubing and remove the faucet. You can buy a small tube cutter for little $. Then install a compression fitting and you're ready to insall the new faucet. Newer faucets usually just have fittings in which you can screw on flexible tube lines (i.e. PEX, braided stainless, etc). So, you secure the flexible tubing to the faucet then secure the other end to the new compression fitting on the existing copper lines. CHECK FOR LEAKS!
Here's a little video explaining how to install compression fittings - easy peasy!
PS, I once had a very bad experience 3 yrs after installing a compression fitting to a copper tube... somehow it *sprung* a leak and flooded the house - a real mess. So, keep an eye on your plumbing!