How does the sea get salt in the water?

Because of minerals carried by rivers.

rivers and streams carry dissolved salts accumulated from themountains and plains.

When rain or subsurface water comes in contact with rocks, the water dissolves a little bit of the minerals in the rock -- a process called chemical weathering. Therefore, because of chemical weathering, neither surface nor subsurface water is pure, instead they contain lots of dissolved minerals. When this water evaporates the salt gets left behind. Now consider the oceans for a moment. Every day millions of gallons of rainwater flow into the sea. Meanwhile, millions of gallons of pure water evaporate from the ocean surface, leaving lots of salt behind. So the ocean can't help but be salty.

It comes up through the bottom. Salt domes in the earth can be huge. There's a salt mine in Poland that's been in continuous operation for 600 years and the dent they've made in the dome is like putting a scratch on a basketball.