Step into the tub and pull the shower curtain closed. Check to make sure that there is no gap between the curtain and the wall at either end. Curved curtain rods arc inwards at the sides to prevent leaks, but they cannot stop water if the curtain is the wrong size or it is not fully extended.
Pull the bottom of the vinyl liner into the tub, but leave the fabric curtain hanging free on the outside side of the tub. Make sure the vinyl liner is tucked into the tub before each use so it can catch falling water and divert it into the tub rather than out onto the floor.
Check for other possible sources of a leak, such as the showerhead. A showerhead can spray water up and over the curved curtain rod onto the floor if the junction where it meets the gooseneck pipe running to the wall is leaky, if the shower pressure is turned too high or simply if the showerhead is angled in such a way that water sprays higher than the top of the curtain rod. Repair or replace the showerhead if it is leaky or faulty at adjusting pressure, and adjust its angle if it is too high.