Rivals mode is a great way to get faster. You can race against someone's "ghost" and see specifically where you are losing speed.
The funny thing is that sometimes people overdrive the car into the corners. Sometimes, slowing down into the corners is actually the way to be faster overall. I beat a lot of rival ghosts by braking earlier in the turns and actually exiting the corner faster. The obvious example is where you have a very tight turn followed by a long straightaway. The key to that part of the track is to get on the gas as soon as possible so you can have more speed for passing on the straight. Driving into the corner hard will just prevent you from getting on the gas earlier. I'll brake earlier, but be able to hit the gas sooner on the way out. My opponent will beat me into the corner, but on the next straight, I'll be carrying more speed out of the corner and will be faster overall.
Thinking about the track and understanding where the most important parts of the track are will go a long way to making you faster. Try braking earlier and getting through the corner smoother, and you'll often find yourself faster on the way out.
Another aspect of the game is setting up the car, and unfortunately there's not a lot you can do if someone else's car is set up better. A lot of players online are just better at setting up a car and are able to drive faster because of it. That's where getting into rival events where the cars are required to be stock can help. On those events, everyone has the exact same car and setup, so it is just down to driving skill. You can learn a lot there. The Top Gear challenge is great for that.
Another tip is to use manual clutch. It will make you a lot faster, especially for the lower level cars.
I think that fact should get me an early release copy, right? 
