by train
There is a red train that runs several times daily to Ãle Rousse, also running by the beach at Calvi and affording wonderful views. Be careful which carriage you choose to sit in--the smaller one has windows that do not open properly and it gets incredibly hot in there. There is also a blue-and-white train to Bastia which appears to be fairly regular.
by car or motorcycle
It is possible to rent Motorcycles and Cars from several places in Calvi, the most notable being Locations Auto-Moto on the Marina you will most likely notice this company by the two Porsche 911s parked out front. Aside from the more expensive vehicles previously mentioned, they also rent family cars, dual-purpose bikes, etc. All vehicles seem to be in great condition and prices are pretty reasonable.
It is worth noting that Corsica's road network leaves a lot to be desired outside of the main tourist centres, with roads either lacking markings, being extremely narrow or having no guard rails over mountains and cliffs. If renting a motorbike, I would recommend going for something that is not averse to a bit of rough terrain; Ducati 999Rs, while lovely, are probably not best suited to the Corsican road system though this does not stop the Italians trying!.Also, many of the road signs are in Corsican only, the French having been scrubbed out thanks to the FLNC or at least nationalist sympathisers, so make sure you have a map that covers both.