Step-by-step guide
One way is to use grib_set with the key "scaleValuesBy". Let's say you have a field in orig.grib whose values you want to multiply by 2.1. First check the original data value statistics:
% grib_ls -p min,max,avg orig.grib min max avg 234.554 312.085 278.977
You could have also checked the statistics by "grib_ls -n statistics orig.grib".
Now let's scale all values up by a factor of 2.1:
% grib_set -s scaleValuesBy=2.1 orig.grib out.grib
And check the new values after the multiplication:
% grib_ls -p min,max,avg out.grib min max avg 492.563 655.376 585.853
For adding or subtracting a constant, you can use the key "offsetValuesBy".