Heat up your tires for more traction
Just as with in real-life, Project CARS is conscious of your tire temperature. It is important that you heat up your tires and keep them as warm as possible for added grip. To do so, you need to push your car around corners as hard as possible without spinning out, and accelerate quickly. You can view your tire temperature with an in-race HUD by pressing left on the d-pad a few times.
Apex every corner
The Apex is one of the most important fundamentals racing. At a basic level it's the optimal line around a turn. What you need to know is that when you hit a corner, you want to start from the outside and cut inside before heading back to the outside. To optimize the line you'll want to slow down to the fastest speed that you can hit the corner at, so that when you leave it you can carry as much momentum as possible upon exit.
Below is a diagram that may help you visualize the concept.
Practice on Nurburgring Nordschleife
Project CARS has a lot of great tracks, but there's one that stands out in particular: Nurburgring Nordschleife. It's a nearly 13 mile long track that includes every type of corner at varying speeds. Due to its difficulty and pleasant design, it is a great track for practicing on and pushing yourself to become better. There's a reason it is regarded as one of the best tracks in the world.
You have control over A.I. difficulty
Project CARS has a difficult slider available in all modes where A.I. is present. If you're finding yourself frustrated, just push the slider to the left. 40/100 is a great spot to start at.
Turn on assists if you're losing control
Assists are available in the settings that can help make controlling cars less challenging. For example, Stability Control will aid in keeping your car from spinning out, while Traction Control will assist in moderating your throttle to deliver as much power to the ground possible without losing traction. As you get better you can try disabling these as you'll be given more control over your car.
Find the Car best for you
There is no best car in Project CARS. They are all different. Try out an AWD car like the Audi R8 to see how you like the additional control before heading into an Aston Martin or BMW to feel out RWD. Feeling comfortable with a car is important to having the control and confidence needed to takeover opponents.
Guiding line can help optimize your line
In the settings you'll find an option called Guiding Line which places a viewable line on the track. This line shows you the optimal route for achieving great lap times, barring the positioning of other racers. Enabling it when doing your first lap around a track is a great idea to get an idea of how to hit corners at the best angle.
Brake earlier when the track is wet
Rain makes it much more difficult for your tires to retain traction. If you're racing on a wet track, you'll want to slow down more than you normally would before hitting a corner or you'll suffer the consequences.
Change up your camera
Sometimes a particular camera type makes it easier to perform well than others. While I prefer the hood camera for hitting corners precisely, it doesn't offer a good view of what's to the side of me. So, I like to change to the third-person behind-the-car view when I have other cars next to me.
Customize the HUD
Project CARS features a fully customizable HUD. I tend to leave it disabled, but information related to placement, lap times, and a track map can be seen when enabled. You can toggle between different HUD presets by press left on the d-pad during a race.
Race with a controller or a wheel
If you're playing on PC, you're best off ditching the keyboard & mouse for a controller. It offers much more precision when racing. Better yet, you can buy one of any number of racing wheels for console or PC which will give you the deepest level of control possible, although there's a substantial learning curve involved.