Right now, my 1972 Buick Electra 225 only gets six miles to the gallon (the engine is seriously fragged). How do I make it perform better? I’m sick of gassing up twice a week.
You don’t.
Start over. I’ve owned two gas guzzlers already and that’s about all I need.
The easiest things you can do, depending on how mechanically inclined you are and how much money you have, are: Change the oil. Replace the carburetor.
More expensive options are: Find a cheap rebuilt engine and switch it out. That should get you up past 15 at least.
My best advice is to get rid of the thing. Find yourself something German or Japanese if your looking for good mileage.
It’s a pre-oil crisis American car. What do you expect?
Hell, be happy you don’t own a Monte Carlo. Those babies got six gallons to the mile! 
I had a 1980 Ford van that would barely go fifty miles on a full tank. I don’t know what the exact mileage was but it only lasted a couple of weeks, the van, that is.
The Electra is a huge car, meaning it most likely has a 455 Buick. '72 means it’s a Quadrajet and points ignition.
The Q-Jet’s your best bet for mileage- while the overall CFM is massive, it has small multi-booster primaries that help the big engines get somewhat better mileage as long as you don’t stick your foot in it.
As for improving it, how much do you want to spend? If you advertise properly, you can probably find some rodder who’ll take the car off your hands in order to slap the big-block into a smaller car, like a Skylark, or even a Nova or Firenza.
If you want to keep it- hey, I’m into big cars too- there’s a few things you can do, if you’re willing to spend some cash.
Yank the carb and have it professionally rebuilt. Try Brad Urban at The Carburetor Shop in California. Yank the points distributor and replace it with a complete HEI unit from a wrecking yard. Replace the plugs and remember to gap 'em to .045" or larger for the more powerful electronic ignition.
Plunk some quality synthetic oil in there, replace the air filter, and maybe install a cold-air inlet to the air cleaner. Blow off the old muffler and replace it with something like a “Turbo” muffler or something- no glasspacks- and if you’re feeling really generous, spring for a true dual exhaust.
This should all get you into the low teens, assuming you have good oil pressure and compression. (If you have less than 95 psi compression on two or more cylinders, it’s rebuild time.)
For a little more time and cash, you can spring for a new cam and lifters… properly set up, it could give you both more economy and better power.
A step above that is having the heads reworked for better flow, dumping on an Edelbrock Preformer aluminum intake, and hey, if cost is no object, pick up a Holley Pro-Jection 4 stand-alone fuel injection system.
All of the above, on a used-but-not-abused engine would very possibly get you into the fifteen-sixteen MPG range in the highway (you most likley have 2.73:1 gears anyway) with some 350 to 360 HP, with nearly 500 ft-lb of torque.
Welcome to the wonderful world of tune-ups. These days, with electronic fuel injection and ignition systems, all most of us have to do is change filters and spark plugs. With an old car like yours, a tune-up is a bit more involved.
First of all, check all filters: air, oil and fuel. A dirty air filter can really hurt mileage. OK, so you can’t really check an oil filter. If you don’t know when it was last changed, change it now, along with the oil. This is a good time to check the level and condition of the transmission fluid.
Next, check the ignition. Check the condition and gap of all spark plugs. Replace if necessary. Check the points. (Most, if not all 1972 GM ignition systems had points. You can replace the distributor with a 1976 or later model to get rid of points. This is a really cheap fix, sometimes cheaper than new points if you go the salvage yard route and can find a 1976-1987 Buick, Cadillac, or Olds with a V8 that still has an HEI distributor in working condition.)
Next, the fuel system. Set the mixture screw to the recommended setting. This can also save a huge amount of fuel.
Total cost: about $100 if you change everything I mentioned. If your mileage doubles, which is quite possible if you’re currently getting just 6mpg, you will get the $100 back in just a few weeks. ROIs don’t come any faster than that.
And keep your foot out of it
Actually, every non-high-performance GM had points in '72. Some 'Vettes and a few Pontiacs had experimented with “transistorized” ignitions- though they still used an external coil- but GM really didn’t have anything truly reliable until the advent of the HEI, which became nearly company-wide standard in '73, then WAS fully standardized in '74.
So any Big-Block Buick HEI from roughly '73 to '76 or so, when the 455 was more or less completely phased out, will work.
Unfortunately, Father P will have to obtain an HEI- assuming he decides to go that route- from another Big-Block Buick. I’m not sure about the small-block Buicks- I know the front cover/oil pump/timing chain cover is not interchangeable between the two- but I know for a fact that Chevy, Olds, Pontiac and Cadillac HEIs will NOT fit.
The Olds distributor, in fact, rotates the opposite direction from the others. (The drive gear is simply run on the other side of the camshaft.)
However, as far as the internal components of the HEI go- cap, coil, rotor, etc- GM is GM, they’re all the same, with minor exeptions. Notably advance weights and springs- not a worry if you pull it from a similar size and type engine- and some later-model units had what they call the notorious “seven-wire” modules. (The “brain” inside.) The 7-wire only fits computerized cars, and has no vacuum advance. Steer clear.
Everything else is good- Checking the filters and such. Good call on checking the tranny too… if it’s got a pile of miles on it, it’s entirely possible it’s slipping slightly.
As far as the mixture screws, by itself that’ll make little difference, unless somebody’s messed with 'em in the past- entirely possible- and they’re way too far out. (If they were too far in, the engine’d have died long ago.)
I mentioned rebuilding it, since the Q-Jet has some internal passages that routinely leak. It’s especially noticible if you have to crank and crank and crank on the engine in the morning to get it going, but it then fires off somewhat more easily later in the day. It’s very common to seal the plugs- they’re internal- with epoxy (I use JB Weld) whether the tech thinks they’re leaky or not… 'Cause even if they’re not yet, it’s only a matter of time.
My solution?..
Lift the hood, remove the radiator cap and put it in your pocket. Replace EVERYTHING that’s not in your pocket with a Saturn SL2.
It’s not the land-yacht you’re used to, but I like mine!
Thanks for the help. I’m going to have the oil changed tomorrow. In fact, I’ll probably make an appointment for a full tune-up.
God bless those big American cars–who needs an SUV when you have one of those, uh?
Doc Nickel and Sewalk, your assistance is especially appreciated. Maybe I could recycle Jeremy’s Evil Twin into biodiesel and use that as an alternative fuel source? 
If you really want a great piece of old Detroit steel, try to find a first-generation Toronado (1966-1969). A big-block V8 and front wheel drive with a strong transmission. Those are the only fwd cars I think are worth a damn. They are all two-door coupes, but with no transmission tunnel, the back seat is plenty roomy for normal-sized adults. And they look great, too.
Funny you mention that sewalk. That’s precisely what I’m working on now, a '66. I’m updating mine a bit, with a later engine, 4-wheel discs (a 5,200 lb car capable of 125 mph running on all drum brakes?) and a host of other improvements.
That’s part of why I mentioned the HEI conversion to Father P- I dumped my points for the HEI and immediately gained a smoother idle and easier starting.
And you forgot to mention the cool rotating-drum speedometer.