Both Antibes and Juan les Pins have train stations on the main Nice-Cannes line.
The usual method of driving to Antibes is to take the A8 and exit at the Antibes exit junction 44 and then taking the winding road down to Antibes. It is possible to approach Antibes along the coastal roads RN98 and RN7 from Cannes and Nice/Cagnes sur Mer. In summer all these coastal roads can be extremely congested as can the main route from the A8. There are, however, very few alternative methods of access and all of them eventually use one of these roads so if you want to go to Antibes then you pretty much have to expect traffic jams.
There is a regular bus service no 200 between Cannes, Antibes and Nice from Place Charles de Gaulle. Alternate buses go to Nice Airport and to Cap 3000, a large, pleasant but quite expensive shopping centre near Nice.
Plane
The Nice airport is the closest airport to Antibes. It is not a long drive from the airport to Antibes.