It depends on how you wish to harvest and eat it.

If you eat the advanced sprouts (more seeds needed) then it only takes 3–4 weeks.
In this case you pull the whole plant out and simply trim the roots off before eating.

If you want to harvest and keep growing then about 4–6 weeks.
(then harvest tips with scissors etc, the stalk becomes less edible)

The best way to grow it fast is either in a grow bed (hydroponic or aquaponic) or in a grow-media tray. Typically water cress does not require soil and grows very well in most well draining (gravel etc) wet media.

Below is water cress grown in a 50 litre tub with clay balls using a aquaponics approach. This is a 50–50 plant and harvest (half tub planted couple of weeks apart). Warm weather and good nutrients and it grows very fast.