Glad you had a safe & fun trip...
To answer your Q.
First plow a groove from end to end in the bottom of the top rail and the same in the top of the pillow rail 1/2 to 3/4 deep. Cut a bunch of slats to length, place them in the grooves, decide on spacing (gap has to be < 4" for child safety), measure the gap and cut spacers (top & bottom) to fit allowing them to be a bit proud. After the glue is dry, (a)level the spacers with a pattern bit. Put the slats back in and stain/paint to suit.
Operational Note:
A lot of glue is going in a one time, so I suggest that after(a) glue up the pillow rail with the top rail tightly dry fitted.
After an hour, glue in the bottoms of the slats with the top rail tightly dry fitted.
After an hour, turn it upside down and glue the top rail and slats together.
If you're working alone, as I am usually, blue tape a framing square to the pillow rail to maintain square awareness.
You didn't ask, but the top rail joints are squared shouldered tenons. Easy with a WoodRat/corner chisel, but possible with a router table. In the bad ole days it was all chisel work.
Joe