My biggest advice is simply make things. A Computer Science background is always nice but the best designers are ones who have always made things. Mods for other games, table top games, just whatever. Make things that show how you understand encounter design and player engagement. It will be rough at first but there are tons of resources online, take advantage of them and start making stuff. As far as starting goes, pick a game you already enjoy and see if they provide modding tools and just start fiddling around with it. Figure out something you want to make and then try to make it. Start small and get bigger from there.