What is the ruling on prayer, and how does one purify oneself from the clear discharge that exits continuously without reason or desire?

The exiting fluid is impure and necessitates Istinja (washing private parts) and Wudu (ablution). If it exits continuously without stopping, then you are afflicted with incontinence, and you must take precautions, such as placing a tissue or similar, perform Wudu, and pray as much as you wish with that Wudu until the time for the prayer expires. However, if it stops for a sufficient time to perform purification and prayer, then you must wait until you can perform Wudu and pray during that time with a valid purification.