A household iron is fine for a handful of patches. Use a dry setting with no steam, press straight down on a hard flat surface, keep a pressing cloth between the iron and the patch, and hold rather than sliding. Turn the garment over and press from the back as well.
A heat press is the better tool for runs of 25 or more. It holds a set temperature, applies even pressure across the whole patch and times each press, so every garment comes out the same. Shops applying patches to hats use a curved cap platen; see our trucker hat patches page for that.
Whichever you use, let the patch cool completely before you test the edges. Warm adhesive is still soft and can lift if you pull at it.