As the navigator of the Straw Hat Pirates, Nami's fighting style is focused on manipulating the weather of her surroundings, known as the Art of Weather. Combined with her extensive knowledge of the oceanography and weather systems, her style can be used to devastating effects.
Originally, Nami simply relied on predicting preexisting weather and using that to her advantage, as seen when she deceived the Tightrope Walking Funan Bros about a storm while stealing their ship. For close combat, she used a simple bo staff composed of three sections that she hid under her dress.
Sometime before the events in Arabasta, Nami explained to Usopp a revelation she had over the course of their voyages. Upon examining the monstrous strengths of the rest of the crew, Nami noticed that she and Usopp were the weakest ones. Seeing as there was no possible way that they could ever match the strengths of Luffy and the others, and that there would come a time when they could no longer depend solely on the help of others, she figured that the only way they could compensate is with the use of their wits and some formidable weapons. She thus asked Usopp to make her a weapon so that she could fight with the others. Upon that request, Usopp went to work on her new weapon and by the time the Straw Hats reached Rainbase, he finished it. He thus gave her the Clima-Tact, a modified version of her original bo staff. This proved to be a very useful weapon in many situations.
Over time, her Clima-Tact has been upgraded into better and more powerful versions from further modifications and acquisition of new technologies. During her stay at Weatheria, she has gained access to its advanced weather technologies and knowledge, including the Weather Ball. Haredas, her mentor during the time, was horrified by the fact that a Weather Ball can be used as weapons when she asked if it could, as such a thing can cause chaos around the world. Her skill in weather manipulation has increased to the point where others believe it to be magic, though Nami herself states that it is simply chemistry.
Before the timeskip, each time after Nami used one of Usopp's versions of the Clima-Tact, she would hit him complaining about some problem with it.