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I have a desktop lathe (Sherline 4100) I use for small metalworking for making quadrotors. It didn't come with an emergency stop button but I found some on ebay.

Why does my e-stop button have four spade terminals C NC C NO?

How do I hook it up?

be careful if you're not used to working with line voltages!

Emergency stop buttons have two switches inside connected mechanically. One switch is normally open NO (and becomes shorted out closed when the button is pressed). The other switch is normally closed NC (and becomes open circuit when the button is pressed).

Why two? To protect against failure. Switches are cheap mechanical bits that get stuck or broken all the time. You don't want your emergency stop to break, so you add redundancy. If either the NO or NC switch breaks, the other one can still do the job.

Easiest way to connect (But not safe! Don't do this!) is just to ignore the NO switch:

That's easy because when the button is pressed it just stops any current from reaching the motor.

But the safer way is to use the NO part too. Now this gets complicated because you have to make it so when a connection is made, it stops the current. So you can do this with a relay, but then you need to control the relay the right way.

I didn't show all the details converting the AC to a DC voltage that's good to power the relay coil. And I showed it with an SPDT relay. But this is better because it only takes either one of the NO or NC switches to stop the motor.

That's better but still isn't best. Best is to have part of it going to the main speed control because you want to make sure that when you turn off the emergency stop switch, you don't want it to immediately start moving again! So it's really not so simple to add an emergency stop to a tool that wasn't designed for it.

Emergency button looks like this inside:

The two C are different. The two switches are linked mechanically but not electrically. OK?

One very crude way of wiring an emergency stop switch is to make it short out the supply and blow the fuse. It's an emergency, right?