Is there any software (preferred free) which allows me to copy a DVD (Disk to Disk copy)? I have installed Burn, but it does not seem to let me do what I need.
You can use the built in disk utility to create and burn images.
There are several guides online about this but this one has pictures!
It really depends what you are trying to do, Toast is the Daddy here but it's not free or particularly cheap.
If you are trying to copy a film, you need either Fairmount or Mac the Ripper (NB MTR is no longer developed and requires Rosetta to run on Snow Leopard) or the commercial Ripit (approx $20). You can also use handbrake for direct to device ripping.
There is also Liquid CD another free DVD programme.