You can travel from the south to the north without problems by car, taxi, public transport, or on foot. There are different checkpoints along the borderline, mainly for passing by car. You have to present your passport, and they will allow you to enter the northern part of Cyprus.
If you want to cross the border without a car, then it makes sense to visit the tourist Ledra Street in Nicosia, where, in addition to cafes and shops, there is a checkpoint - a pedestrian crossing from one part of Cyprus to another.
How to get from Larnaca Airport to Girne on your own?