They travel by steamship from England to the African coast, where they then take a smaller boat up the river to the location of the Porter's camp. It's important to note that Clayton, the antagonist, is not in the original novel. He was created for the 1918 film adaptation.
In the 1918 film adaptation, the character Clayton, who is Jane's fiancé, accompanies her and the Professor to the jungle. They travel by ship to Africa, and then by canoe up the river to their destination.
So, depending on which version of "Tarzan" you are referring to, the method of transportation to the jungle can differ slightly.