Doublespeak is language that perverts true meaning and purposefully making things ambiguous, while euphemism is language that "softens the blow". Doublespeak is often found in political speeches, where they intentionally make things very longwinded or professional-sounding, when it is in fact futile talk, or conceals the true essence of the speech (sometimes directing the focus on something very insignificant to achieve this). An example of this from a certain Alan Greenspan:
"It is a tricky problem to find the particular calibration in timing that would be appropriate to stem the acceleration in risk premiums created by falling incomes without prematurely aborting the decline in the inflation-generated risk premiums."
Note that the above is not euphemism as such.
An example of euphemism would be replacing the more pejorative term "old/senile" with terms such as "chronologically advantaged", which sounds much more polite. Euphemism can be used to intentionally mislead readers/viewers as well, in which case it may serve as doublespeak.