In general, though, there are some fundamental rules to being quick in this game, the first of which is that you have to be aggressive. Most races have around 16 competitors in, and if you don't take part in qualifying, you'll have to start from the back of the grid and carve your way through the pack.
Of course, some circuits are easier to overtake around than others, but passing in this game isn't easy, not by a long shot. The car ahead will always make their rear bumper as wide as possible, especially if they're your nemesis or rival.
Although you need to be aggressive, you can't be foolhardy, steaming into the first corner where you can only squeeze three cars abreast when you're number 4 won't end well. You have to pick your moment to pass, if you have time, use it to your advantage.
If you're in a gaggle of cars, think about feathering the throttle to drop back and position yourself better for the upcoming corner and always use the slipstream to your advantage. Sometimes you have to sacrifice the first corner of a complex to be fast through the rest, that's the art of racing.
If things do go pear-shaped, though, you have the option to use a flashback and rewind your mistake out of the race, we won't tell anybody if you use them regularly, we promise!
The final point is something that a lot of players won't have even considered, go amiss for most players, particularly those that are less experienced. The handbrake turn is something that can't be overestimated in slow-speed and tight corners. Press circle on PS4 or B on Xbox One to put the handbrake on, your car will turn on a sixpence if you try it. Be careful not to use it when in a crowd of cars or to use it too much and spin. You'll be needing those Flashbacks again if it goes wrong, but the handbrake turn is often the fastest way round a tight corner!