Using a Digital Multimeter for the first time

After 15 years of service I replaced my old voltmeter with a Radio Shack Digital Multimeter.The instructions read that the amps should be turned off when inserting the leads. This would mean that after playing the amp for 2 hours I would have to turn them off insert the leads and then turn the amp back on.I doubt if I could get an accurate reading this way but Radio Shack says I could.So,I ask for your opinions.
Thanks all
Sorry you had trouble but the advice was correct.

I have made 10's of thousands of voltage measurements on live circuits with all types of analog and digital meters and never smoked anything. Properly used there is no way a digital meter set to volts could cause smoke. Impossible. The most logical explanation is you accidentally set it to measure current as you turned on the meter

You should have the meter on and then insert the leads.

You really should open it to inspect for damage and replace the part that smoked.
Herman> your advise was absolutely correct.I may have done something inadvertently that would cause the problem.
I still dont understand why the instruction manual would read that the amp should be off when attaching the leads of the Digital Meter.Wouldn't this defeat the purpose of biasing an already heated tube.

they put that blurb in there for safety reasons. It would be more correct if you would measure it like you suggested.
The reason you would want to change the smoked component is that it will have latent failure associated with the smoke and eventually derate its performance. Over a period of time the heat and increased resistance would eventually breake it down until it will no longer function and you would be wondering what happened.
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Voltage on a digital multimeter looks like an open circuit to the circuitry you are trying to measure.  Therefore, it can't hurt the measure while the circuitry is "hot" as long as you are in the correct setting.

If, however, you inserted the leads with the circuitry on, but the multi meter off, you ran the very real risk of a short circuit when turning your meter on.

it looks like the OP made the simple but easy to make mistake of shorting the circuit by having the multimeter on the wrong setting.  Either Ohms, or current, and not voltage. 

I can't think of one Engineer or Technician that I know, including myself that has no fried a circuit by not paying attention to the setting on the multimeter.

I would open the amp (unplug it first) and do a very close inspection of the circuit boards to see if there are burned traces or components.  Look closely.

Something was going bad and fried, or partially fried.

take a look.