I have a 05 Buick Tarrasa. When I fill it up at the pump, taking 20 gallons in a 21 gallon tank, the gauge only goes to half, or 2/3 full. Sometimes I shut it off and the gauge will go to the full mark. The last tank I put in 17 ½ gallons of gas, and got only 270 miles. Some freeway driving and some city driving. The worst I ever got was 17 to 18 mpg.

When I filled up and took 20 gallons, the tank showed 1/8 full. The computer gives information on what the tank reads. A full tank had shown 350 to 400 miles based on the past mpg. Now it will only show 240 miles on a full tank. Of course the warranty just ran out. And how do they do that?

Sounds like the fuel float in the gas tank is messing up. Best thing to do if you can't afford the gas tank to be taken off and a new fuel float installed is to use your trip meter and fill up every so many miles. When I had to get a new fuel pump installed in my Jeep Cherokee a few years ago the gas gauge still reads full even after I've driven 100 miles out of the tank - then it drops to 3/4 full in seconds! I use my trip meter and fill up every 130 miles or so and just ignore what the gauge reads anymore.

It just started working again. Could it be someone was trying to get gas from my tank and the syphon hose hit the float and got it stuck?

When you fill your tank up, your fuel tank sender may be "seeing" an open circuit when the sender finger moves too far and goes off the end of the card.
There is a new GM part number available to correct this concern and there is a possibility that it could be subject to a special policy replacement at no charge to you.
Contact your nearest Buick dealer and tell them what has been happening. If they deny you any assistance, ask for the General Motors Customer Assistance toll-free number and seek help from them.