There are a few things that will cause it, so they are listed in order of how common they are. I have considered carbureted engines, fuel injected engines, engines with distributors, and direct fire ignition system equipped engines to help ensure that this will help anyone who has this problem. Except for charging system problems, which would set off a host of other signs and warnings pointing you straight to the problem. When an engine stalls there will be one of (or a combination of) any of these problems which are normally ignition system and fuel system related. Of course, not all stalling problems are related to these systems, as simple things like driver error, or transmission problems can make the engine die, too. Check out this list of things that will cause an engine to stall, and what you can do about them.
Incorrect idle speed
On fuel injected engines, the throttle is completely closed while it is idling. That is why there is an Idle Air Controller (IAC). These things wear out and stick. As you can see, it is #1 on the list, therefore the most common. To test the IAC, you can create a vacuum leak by unplugging the vacuum booster hose. If the engine runs better, then the IAC is not opening or is clogged. If the engine speed doesn't change, then the IAC is not the problem. On a carbureted engine there are 2 idle speeds. First make sure the fast idle and choke are operating properly, then adjust ignition timing and idle speed to factory recommended specification (around 800 RPM, usually).
Clogged fuel filter, or bad gas
This is self explanatory. Remove the fuel filter, and blow through it. Is it free flowing? It should have very little resistance, but you can feel it. If there is no resistance at all, replace the filter..it is blown out. Also, if it is clogged, obviously it needs to be changed. You should also get a glass (or something clean) to catch a fuel sample from the line. Just turn the key on, and you will get about 1 second of burst from the pump, if it comes on.
Damp or damaged ignition system components
Did it just rain? If your engine has a distributor, you need to remove the cap and spray some WD-40 in it to push the water off the terminals and rotor. Especially the triggering device that is under the rotor. It needs to stay completely dry at all times. If any dampness gets inside the ignition system, it will short everything out. Think of plugging in an extension cord and placing the other end of the cord in a glass of water. It is the exact same principle.
Bad, fouled, or incorrectly gapped spark plugs
Pull the plugs and look at them. The electrode that comes through the center needs to be 'squared off' looking and clean, with sharp edges. If not, the plug is worn and needs to be replaced. If it is fouled, other problems exist on the particular cylinder that need to be corrected.
Emissions system malfunction
This is the easiest one. Is the engine light on? If you have a 95 and up model vehicle, you can take it to Auto Zone or Advance Auto Parts for the free diagnostic scan. If you still need help after that, you can find the link around here somewhere, that says talk to a mechanic or something like that. This would be for specific troubleshooting procedures for your vehicle. If you have a pre-95 vehicle, then you can go to troublecodes.net for procedures on how to get the codes out of the computer.
Bad spark plug wires
Run the engine at night, is there an eerie blue glow around the wires? Replace them, they are leaking. Another more technical way to do it is with an ohmmeter. Measure the wire with a tape measure. The wire resistance should not exceed 4,000 ohms per foot of wire. Example: If an 18 inch wire has 6,000 ohms, it is still good
Vacuum leak in the fuel injection system, intake manifold or vaccuum hoses
Vaccuum leaks can be elusive. By far, the best way to find a vacuum leak is with a 'smoke test'. The system is filled with smoke, and it comes out where the leak is. It takes about 20 minutes, worst case scenario. Another way to find a leak is by spraying some carburetor cleaner in the areas around intake to head mating surfaces, port injectors, vacuum hoses, throttle body, etc... When the engine runs better, you have found the leak. If you have exhausted these methods and still come up with nothing, then the 'health' of the engine will need to be monitored with a vacuum guage. There could be excessive carbon inside the engine or a worn timing belt. Vacuum guages cost less than 20 dollars.
Torque converter is not unlocking
Does it die when you hit the brakes, before you even completely stop? The torque converter is not unlocking like it should to let the vehicle stop. The torque converter is what couples the engine to the drive train. When it is locked in, vehicle speed is directly related to engine speed. If it doesn't unlock, the vehicle speed will suck the engine speed down to nothing. A quick test for this is to put the transmission in neutral, when you slow down. If it acts right, then the torque converter control system will need to be inspected. When you put the new trans in it, also install an external transmission cooler, and it won't happen again.The important thing is to get that fluid out of the radiator, or tend to the cooling system problem in the engine. That is what burned it up.
By now, you should have found out what keeps making your engine stall. If you still need help, then feel free to contact me through my profile. I'm glad to help and all you have to do is ask. Thanks for reading!