The best and almost only way to Cap-Haitien is arranged tourist tour by bus (or Caribian cruiser)...atleast I wouldn't rent a car there but you can always try local Tap-Tap buses, colourful and not really comfortable....all the streets are in bad condition and the traffic in Cap-Haitien is crazy...
There isn't are no railroads on the island...
I would recommend air travel no matter where you are coming from, as the road from the Dominican border to the city is mostly unpaved, and the road from Port-au-Prince is precarious and in bad condition. (Flights from PAP to Cap range from 20 to 40 mins, travel by road takes from 6 to 10 hrs!!)
Cap-Haitien has a variety of ways to get around. You can take a tap-tap, a converted pickup truck with a wooden roof and benches in the bed, which is the cheapest way, with prices at around 2 gdes. (around 7 cents), but overcrowding is common, and it is very uncomfortable. Taxis are typically 5 dollars Haitian per person, around a dollar American, but be advised that rates go up when venturing outside city limits, and rates may fluctuate wildly due to recent political and economic instability.
The best way to get around in my opinion is in a rental vehicle, preferably a standard transmission 4x4.
As the ride by car fron PaP takes about 8 hours it is better to pay USD 110,- for a return ticket with Caribinter and take the plane.