Hi Ernest,
Here is a good document on how all of this is done (it's called handshaking, and the switch and DMM send triggers to each other when each one is done doing its job):
http://zone.ni.com/devzone/conceptd.nsf/webmain/6daaebb0952e54b386256e3700808423
I know it's a lot of reading, but it could be useful for your application.
There is then a good example of this in the example finder using the NI-SWITCH API:
Help >> Find Examples.. >> Hardware Input and Output >> Modular Instruments >> NI-SWITCH >> niSwitch DMM Switch Handshaking.vi
With the information above and this example, you should be well on your way to getting these two devices to work well with each other.
mike