Perpetual Ocean by NASA [video]

The moon does have a effect on Earth's oceans, but the biggest reason why oceans are active, is the variation of temperature both in the atmosphere and in the water(This also creates a variation on pressure). The difference on air pressures, will create wind, which in turn create waves.

Ocean currents exist because different places on Earth are at a different temperature, and therefore the water will feel a pressure force to go elsewhere.

This is quite a generalization, but meteorology is a complex science, and there is much to dig in.

Some currents, like the Equatorial Counter Current (NECC) (which runs West to East just North of the equator) are actually wind-driven surface currents.

Yes it's about the wind (geostrophic currents) and temperature, but mainly because the earth doesn't stop rotating! The resultant forces are different depending on the latitude and depth. Note the dramatic differences on either side of the equator.

The most famous of these uneven forces is of course the Coriolis effect.

It's a visualization of the data produced by the ECCO2 project (http://ecco2.org/), which feeds all available measurements of temperature, current, etc. into an MITgcm fluid-circulation simulation model (http://mitgcm.org/), which then estimates the most likely circulation.

Lots and lots of physical measurements. One large scale example is the Global Drifter Program. The US contribution is largely funded by NOAA.

http://www.aoml.noaa.gov/phod/dac/index.php

The array is usually maintained at above 1000 discrete instruments deployed by various cargo ships, and research vessels globally. These measure ocean currents centered at 15m depth, which helps eliminate bias from surface currents driven by winds. These drifters also measure surface temperature some with sea level air pressure.

Ocean currents have been well known and used for shipping for hundreds, if not thousands of years.