Properly? Ironic choice of words.
GTA is designed to allow players to enjoy it in a variety of ways. Goofing off enjoying causing mayhem, or seeing how much police escalation you can experience and/or escape, are certainly popular choices.
The game has a very long list of statistics in keeps and shows, which is like a menu of things you might enjoy trying to do, or might not care about.
I’ve tried playing it in a number of ways, including trying to be as non-violent as possible or following various self-imposed moral codes (e.g. self-defense only).
However as @Mimishu1995 and @Darth_Algar pointed out, there is one main expected way the developers designed into the games, which is to follow one or more canned plot-lines that mostly involve doing various errands for organized criminals. They each usually have in mind for you to do some challenge, which sometimes involves a doublecross (so you actually have to escape to win) which leads to the next offer of a mission from someone. Some of the missions “unlock” more of the game world, so for instance in GTA 3, the city has parts you can’t reach until you complete certain crime missions, and also other criminal groups, vehicle types, locations, weapons, population types, and so on are added to play the more of those missions you do. While the games are ultimately about exploring and trying things and doing crazy things, they usually tie up a lot of the content in those scripted missions.