The hat pattern you shared is worked flat and after you work the ribbing it says:
Change to Stockinette stitch.
Kl row Pl row.and knit for 24 rows.
K1 row P1 row is explaining how you do Stockinette stitch. You alternate knit rows with purl rows so that all the smooth part is on one side and the bumps on the other. You are to work that way: knit and row, purl a row for 24 rows.
If you want to make a baby hat with sport weight yarn I think you will want more stitches than this pattern gives. And probably the row gauge will be different, so you would need to work more rows than 24 to make it the length it needs to before the decreases.
The "basic hat recipe" that Sue pointed you do might be your best bet.