You’ll see a U-shaped curve that represents the crotch curve from your template. Pin the sleeves together along this curve, and sew using a stitch suitable for jersey knit. Sew again along the bottom of the U using the same stitch–crotch seams get a ton of hard wear, and they’re much easier to sew strongly the first time than to mend later.
Straighten out the shorts, removing one shorts leg from inside the other, and you should easily be able to see the shorts’ waist now. Fold the top edge of the waist down about 1″ to the wrong side of the shorts and sew it to form the waistband, leaving a couple of inches unsewn to insert the elastic.
Take your child’s waist measurement, and measure out a length of 3/4″ or 1/2″ elastic to exactly that length. Pin a safety pin to one end of the elastic, and use that end to thread the elastic through the waistband. When the elastic is completely inserted, overlap the ends, sew them together very strongly, re-insert them into the waistband, and finish sewing closed that last opening in the waistband.