How do you remove a front catalytic converter on a 02 Mercury Sable 3.0L?

If the car runs for a while and then stalls you should suspect that internal parts of the catalytic converter are lodging themselves in the exaust pipe between the first catalytic converter and the second or between the second converter and the exhaust pipe muffler. When the catalyst chunks partially block the hole the car will stall. To test, try opening the exhaust after the first converter just enough to make it really loud and try driving it to see if the problem disappears. If it does you will have to remove pipe sections until you find the catalyst chunks and remove them.

The catalytic converter is part of the exhaust system, which is the air running out of your engine. The engine does not need to come out to remove it. Look under your car. Your exhaust pipe comes out the back. Follow the pipe back toward the engine, past your muffler (which is a big box) and you will see a foot-long section of the pipe that is larger than the rest (but still round). That is your catalytic converter.
Sometimes it will be covered by a heat shield (a piece of metal that keeps the extreme heat of the cat. away from everything else.

Step one: Jack the car up and place it on jack stands.
Step two: Let the car cool down a little cause the exhaust is extremely hot and will burn you.
Step three: locate the bolts that hold the catalytic converter onto the other exhaust pipe pieces (this will be easier if you have the new one so you can see how long it actually is.)
Step four: Spray the bolts you need to loose with penetrating oil ($3 at the auto parts store). These bolts are going to be VERY hard to get off because they are rusted and they are used to being hot. If you can use a six point socket, that will keep them from stripping. You can also heat the bolt up with a torch (until it glows orange) and this will make it easier to move. Be careful.
Step five: remove the oxygen sensor that is attached to the catalytic converter. This will just look like wires coming from a cylinder that is sticking into it. Unscrew the cylinder (I recommend an oxygen sensor socket as this bolt is quite difficult too, especially when cold. Don't heat the oxygen sensor with a torch or you could damage it)
Step six: Unbolt the catalytic converter (now that you have sprayed the bolts with penetrating oil and let them sit for a few minutes.
Step seven: Place the new catalytic converter in the old one's place, and do everything in reverse.

The best advice I can give you is be safe, and don't give up. automotive repair is about perseverance as much as know-how. When you come across that bolt that just won't budge, keep working at it and try to think of different ideas (like a breaker bar, or drilling it out with a drill). You can do this job!
I've attached a video that I found. It may be helpful.

Bank 2 is at the front of the car.

Most likely it is the catalytic converter one the firewall side clogged. the part that melts is the exhaust feedback side and it backs up the hot air once the converter is clogged. I had same problem on 03 escape. Also resist putting straight pipe on downstream converter because it catches any loose carbon from going into the muffler. If the muffler is clogged it will do the same.

You will, in all probability have to get under the car to see it-you have one in front of the catalytic converter (each side) and one behind the cat (it doesn't really affect how the car runs, it only monitors the car efficency)-the O2 sensors are perpendicular to the exhaust pipe and have a 4-wire harness connected to it. they look like this:

http://www.partsgeek.com/catalog/1998/ford/taurus/fuel_injection/oxygen_sensor.html

Here ya go....

Two are in each exhaust pipe near the connection to the header and two are at the outlet of each catalytic converter. Upstream and downstream.

IF there is another (and I am pretty sure there is) it should be on the exaust manifold..

Please dont forgt to rate well ;o)

yes there are 4, the 1st two small ones are called "light off cats", the 2nd two are the main cats

Yes the front O2 sensor(the one before the cat) could be lazy and cause this also.