When you select your race strategy there are 2 things you can do.
1/ Adjust your stints so you control what lap you carry out your pit stop(s), and what tyres you fit. Or you can leave at default.
2/ You can select your fuel strategy. There are 3 fuel settings, I can't remember their names off the top of my head, but they will be something like Aggressive, Standard, and Conservative
a/ Aggressive - Your car is well under-fueled - This makes the car lighter and faster, but you will definitely need to use a Lean fuel mix for a fair amount of time during your stints. Too much time at Standard or Rich mix and you will not reach the end of the race
b/ Standard - Your car is slightly under-fueled - The car is heavier and slower, but you can spend most of the time at Standard mix, and use Rich mix now and then, but it is best to spend at least some of the time at Lean mix when additional speed or acceleration is not required.
c/ Conservative - Your car has plenty of fuel, you generally don't have to worry too much (if at all) about your fuel burn. You can spend a lot more time at Rich mix - You start with heaviest and slowest car due to the fuel you are carrying, but don't really have to run a fuel saving strategy.
No matter what you pick before the race, under all modes you will burn more fuel if you always run your engine revs into the purple and especially the red zone. You will save fuel (and tyre wear) if you change gear in the green rev range, or short-shift up to the next gear early when max acceleration isn't required.
You will also save fuel if you coast and use your brakes into corners, rather than rapidly dropping down through the gears, using engine braking. I mean brake heavily and drop the gears appropriately, don't over-rev the engine by trying to use your gears as your main stopping power.
All of the above is dependent on the situation you are in at the time. If you need to get past someone and need rich fuel to do it, then do it. Just try and compensate afterwards, especially if you are short on fuel.
Keep and eye on your OSD, and always trying to keep you fuel remaining counter at +1 Lap throughout the race.
Cheers