Coming a bit late since OP but that might still help people.
Challenge yourself. That's very important. I see a lot of people saying they're not fast enough complaining as soon as you get comfort tyres on anything a bit powerful, and they never improve themselves. You got to step out of your comfort zone and eat some dirt and walls. Try a Yellowbird on comfort mediums with no ABS. Try to do some drifting. Take some good old underpowered lemons in open lobbies so you just can't overtake in straight lines.
But don't go that extreme at first, you have to be patient and start with something you actually have time to understand (and I think this is even more important in real life). You want to begin with a car that has progressive reactions so you can build up reflex and instinct. You want to trigger some situations as well, that's why I suggest doing some drift exercises, especially for people who just got a wheel.
A good combo for learning I always ask beginners to try out is the Mazda RX-7 GT-X (FC) on comfort softs on Tsukuba. With these tyres, the car is not overly powerful but still has enough to work out throttle control, suspension is soft and progressive so you'll have enough time to feel what happens and understand why. With this, you can already work a lot of things out : try to slide it just a bit with little angle, try to keep the rear tyres smoking for nearly a whole lap by linking the corners, then try not to drift at all. When you feel at ease, you can then increase the power, harden your suspension, change the tyres, get to a faster track...
Also, an exercise I asked potential recruits to perform when I was in a drift team : try to do a lap as fast as possible while not drifting at all, with the car the guy used to perform drift manoeuvers (so usually very powerful, specifically set up and with comfort hards
). Now that would be a very good thing to do for training when you're confident under "normal" situations, as the window between oversteer and understeer is very small, requiring to refine your inputs.
In general, drive stock cars or cars with no setup as much as you can, because if you constantly tweak your setup, it's not the driver that will improve. You have to be able to adapt yourself to the situation, because you won't be able to adapt the situation to yourself once the race starts. So drive cars in stock form, and / or try to get setups from "aliens" (you will probably ask yourself how they can even stay on the road with that) and get used to it. And drive a great variety of cars and tracks ! Unless you're experienced, consistent, and have support from team mates or any exterior view / references, bashing a single combo for thousands of km will be frustrating and counterproductive soon, and I advise against it unless you're doing some serious competition. Progression at the begining is fast, but soon decreases and stops, at which point you'll be either comforted into thinking you're doing it perfectly and chisel bad reflexes into your muscular memory, which will get hard to get rid of after, or try random things and see your lap times increasing for a while. In short, you will get something like 95% or even more out the first 300km or so, and then struggle hundreds, even thousands of km maybe, to notice some kind of progression again. Usually, this happens for me quite suddenly after a break to purge some of the "bad stuff" (and by break I don't mean a 1 hour break, more like several days at least). most I've driven for a combo was about 5 or 6000 km in 3 weeks, but I've seen people drive even more.
Mentally, I basically have two motos : "ho, if that guy managed to take this corner at that speed, then I can at least go as fast there", and "if I'm not dead yet, I didn't tried hard enough". The wonderful thing in video games is that you can crash as many times as you want without nasty consequences, which means you can progress faster than in real life. Thing is, you can't know where the perfect braking point is until you braked too late. If you never missed, then it means there's still some margin. In real life, you have to do it quite progressively as you don't want to fail harder than missing the racing line or ride a bit of grass, but in video games you don't care, so you can work it out faster.
Of course, a wheel, at one point, becomes mandatory, no matter what some can say or what apd times they can show you. I know a guy who was utterly fast with a pad. He finally made the switch to a wheel, and 6 months after, he was at GT Academy. No matter how fast you are, there's a lot of precision and feedback a controller will never be able to provide.
But all of the above will bring you absolutely nowhere if you don't enjoy it. That's the most important thing. There can be some frustration, anger, competitiveness, but there but still be some kind of fun in the background. I'm even on the edge of saying you have to be a bit masochist to be able to do all that. But then, if you express the wish to be faster, I think you have that thing that will push you forward no matter what, that thing that will make you come back at it even when you raged quit your training session two days ago, not because you have to or someone asked you, but because you can't stand not doing it anymore.