Practically all public transport goes through the train/ferry terminal Knutpunkten Helsingborg C, including regional and long-distance trains and buses as well as local buses.
Skånetrafiken (http://www.skanetrafiken....) runs the local and regional bus and train system, and if you intend on spending some time in the Skåne-region it is highly recommended that you get the so called Jojo-card which is a prepay card that gives you 20% off any ticket. Additionally a duo/family ticket will give you another 10% off for up to 2 adults and 3 children.
By train
Regional trains stop at Helsingborg C and has two more stops within Helsingborg, including Maria to the north and Ramlösa to the south. Generally this isn't the best option for getting around the city as these stations are mainly for daily commuters to farther destinations in Skåne and Denmark.
By bus
Bus is the main means of transport in town. Buses run from early a.m. 'till around midnight and a little later on Fridays and Saturdays. The bus system connects most of the city and all but one #2 stay within one fare zone. Single trip costs 19 SEK, but it's not possible to pay with cash on the buses.
By taxi
Taxi rides are rather expensive in Helsingborg and there is little competition. They can be found right outside Helsingborg C main entrance, next to the Marina Plaza hotel.