That appears to be a standard PVC ball valve. Take a trip to a plumbing supply house or a big-box store, and grab a couple different PVC fittings and pieces of pipe that measure as reasonably close as possible to the internal size of the open valve end. Use a tape measure or internal/external caliper to match the diameters.
When you get back home, find the fitting or pipe that press-fits reasonably firmly into that ball valve end. That's the one whose pipe size you should use to come out of the ball valve.
Keep that pipe size on to your yard drain. Use typical PVC primer and glue to attach the pipe to the valve. You might also consider a PVC union of the same size pipe to allow removing the drain pipe from the ball valve easily if you ever need to.
You may also have to build supports along the drain pipe so it maintains the usual downward slope that plumbing drains need. 1/4" per foot is what USA code requires inside a house, so that's probably a good goal for your drain pipe, too.