How do you shut off the service engine soon light on 1999 blazer?

It will do no good to turn it off, It will just come right back on if you didn't fix the reason and problem that made it come on.

There is a problem with the emission system or Transmission. You need to have the engine scaned with a OBD2 enginer scanner to see what is wrong. Some parts stores will scan it for free just call some and ask them if thay can scan it for you. You will need a scanner to turn it off.