First of all, you cannot ‘put out’ or ‘extinguish’ a star. You can only extinguish something that is burning. The source of a star’s energy is the fusion reaction going on in their core. The only way you can stop a star’s nuclear fusion is by depriving it of it’s main fuel – hydrogen. As for your second question, water will only make the star to glow brighter. Water adds mass to the star and also gives some extra hydrogen. So there is no way you can extinguish a star instantly. On the other hand, you can hasten the nuclear reaction inside the core by adding up more mass to the surface of the star. In that case, water will do the job. But if you stay around the sun with a water hose forever, you won’t survive the supernova after that.
Do you mean ‘staying around a massive sun?’. I don’t think our current sun would go supernova. Only stars with masses above the Chandrasekhar limit will explode as a supernova. With the current mass, the sun would eventually collapse and become a white dwarf.
As @coolnclever suggested, speeding up the nuclear fusion in the core by adding mass to the star is a good way to begin with your efforts to put out the star. But if you could remove the mass from the star, you won’t need any of your ‘extinguishing material’ to put it out. As you keep on removing the mass from the surface, the density of the core reduces and at a certain point there won’t be any fusion happening at all.