How do neurons send electric pulses even though they are surrounded by liquid which is mostly water?
Neurons have sodium, potassium, as well as some calcium channels all over the surface of the cell (I'm giving a very generalized explanation here). The "electric pulses" that you are mentioning is more of electrostatic potentials generated from the interactions of cations and anions flowing in and out of the channels. Water at the specific pH surrounding the cations is a good conductor of these electrostatic interactions.

You have to remember that there are large negatively charged anion proteins inside the neurons which attract the cations (sodium ions for example) to rush into the cell. Once threshold is reached all gates open and an action potential is produced.