Helsingborg is easy to reach from across Sweden and from Denmark. The central station sits right by the harbour, with frequent trains to Malmö (40 minutes), Gothenburg (2.5 hours), and Stockholm (4.5 hours via Gothenburg or Hässleholm). Buses run the same routes at lower prices.
The most distinctive way to arrive is by ferry from Helsingor — the crossing takes about 20 minutes and ferries depart every few minutes throughout the day. ForSea operates the route with large car ferries. The Helsingor terminal is right next to Kronborg Castle, so you can combine the crossing with a visit.
The nearest airport is Ängelholm-Helsingborg (AGH), about 30 kilometres north, with domestic flights to Stockholm. Copenhagen Airport (CPH) is about an hour and a half away by train via the Oresund Bridge and offers far more international connections.