I just discovered how to do it myself a few weeks ago when I was having check engine light trouble with my wife's '90 300TE.
Over in front of the battery there is a little black rectangular box attached to the firewall. It has a protective plastic cover you can remove by pulling straight upwards.
Inside you will see a button, an LED, and a bunch of wire connections (pin sockets).
What you do is while the ignition is in the run position, (with the engine running or not), you push the button and hold it for 3 seconds. Then you count the number of times the LED flashes. Sometimes on mine it doesn't seem to work the first time, but the second time it always does.
Flashing once means there is no fault. All the others mean something or other. I've attached a file that gives the mapping of these codes to faults using the LED.
To reset the code you hold down the button for 10 seconds once you've read the flashes.
There are other sets of codes you can access using the other pins in that connector. If you get to it I can tell you how to access them as well.
There's a lot of other good stuff on this in other threads, but I was mystified for a while before I got some basics down.