First break down(s)

If it's a slant 6 you have a bit of a hassle, if it's a V-8 it's a little easier. That is, IF it's your fuel pump.....

Your best bet is to try and duplicate the problem and check for spark first. Those damn ballast resistors go bad and can cause this problem (it's that white ceramic thing on the firewall with 2 wires going through it...), next up could be the ignition module (flat box, either black, orange, or natural silver with a 5 wire plug....). To check if it's fuel when the car dies pop off the air cleaner lid and pump the throttle linkage once or twice while looking directly down the carburetor throat. If fuel sprays, look else where. Crank it with a plug wire held against ground. If there is no spark, there you go.

If it is the pump, you would do well to try and pinch off the inlet line from the fuel tank before dis-connecting it or you'll have a steady stream of fuel running out. Vise grips work in a pinch, or just stick an old spark plug in the line. Let us know what you find....