Note: I'm no expert at cars.. in fact, I almost always turn to a mechanic to fix problems or do routine maintenance. But here's a list of common problems I've encountered that have adversely affected my gas mileage and caused me to spend more on gas than necessary. Hopefully, these tips will help you get the most out of the $4-5 you're paying for gas these days.
First, you want to go to Fueleconomy.gov and search for your car (by make, model, and year.) Look at the EPA estimated MPGs as well as the self reported ones. Track your gas mileage by tracking the # of miles you've driven using the trip odometer and resetting it when you fill up. Do this for 3-4 fill-ups, then divide the total # of miles by the total # of gallons you've pumped (don't just average all 4 which is inaccurate if you've not driven the same # of miles on each tank.) Is your gas mileage in line with those figures or on the low side? If so, read on.
Common Problem: Underinflated tires.
Check your owner's manual or the side of the door for the recommended tire pressure settings. Inflate your tires to the recommended pressure or slightly higher (but below the tire's maximum pressure.) It's best to do this when the tires aren't very hot otherwise the tire pressures will be biased up. Slightly overinflating the tires means you can go longer before you need to reinflate your tires again. A single tire that's vastly over or underinflated than the rest may also cause your car to burn unnecessary fuel when cruising, so try to keep their pressures fairly even.
Common Problem: Dirty fuel injectors.
Many mechanics will try to sell you this service to clean your fuel injectors for over $100. Most of the time, it's a scam and unnecessary. You can fix it for only about $10 to $20 using Chevron's Techron Fuel Injector Cleaner. (If there are no Chevron stations in your area, just buy some from Amazon.) Just run your car until the gas gets so low the low fuel light comes on or is on the "E" gauge and pour the Techron into the tank before fueling the tank to 100%. Then run that tank to near empty again before refueling.
Common Problem: Excessive engine warm-up in the morning.
You've probably heard a cold engine gets lower fuel economy and this is true! But you're not saving much money by purposely warming up the engine in the morning since it's gonna use up fuel in the process. If you start driving right away, your engine will still use more fuel in the first few minutes of driving because that extra fuel is being converted to heat which warms up your engine. Once the engine is heated, less energy is escaping as heat, so you'll be achieving normal fuel economy. Unless temperatures are drastically below freezing, there's no harm in skipping the engine warm-up and you'll be saving some time anyways.
There are probably dozens of other tips that can boost your fuel economy but they're either dangerous (like hypermilling), expensive, or not really worth the trouble. If you've got more tips, please share them in the comments!