When in town, tap the icon that appear above the cars. Send the cars to the places they need to travel to earn free coins and diamonds. Build decorations in the town to earn coins. Use a combination of fast and slow earning decorations. Although the fast decorations reward you with less coins, you can collect from them often. The slower decorations give you more coins each time they are collected. Save your diamonds until later in the game, when you have more opponents and the tracks have larger rewards.
Practice races
Win practice races to get rewards that include paint jobs and and accessories.
Quick starts
Tap the accelerator exactly when the "GO" message appears, and not any time sooner. If done correctly, you will get a boost at the start of the race.
Tasks
After you have stopped playing awhile, vehicles will begin sleeping in their pits. Tap them to wake them up and allow them to do things again. You will also earn experience points for doing this.
Tricks
You can add various tricks while racing to boost your race stats. However, you must do this correctly. Tap the accelerator pedal at the correct moment, or follow the directions to swipe correctly. This will result in extra experience points and a speed boost.
Turns
When approaching a dangerous turn, slow down. A speed boost will usually follow the turn, allowing you to actually increasing your speed by slowing down. If you do not slow down you will have a risk of crashing.
Upgrades
The garage at Radiator Springs allows you to upgrade your cars to increase their power, and have more chances at winning extra races. Because you only can have one car at a time there, and the waiting times increase progressively through the levels, plan ahead and constantly upgrade all your cars. Do not add too many tricks and decorations to each track too soon. Certain races require a specific number of things that must be made before you can start them. Do not spend coins or gems on things that will not progress the game.
Coins and diamonds...