"They are doing it themselves."
Translation:De gör det själva.
Själv is not only used for constructions with reflexive verbs, but also alone to mean by oneself or alone.
Behöver du hjälp? (Do you need help?)
Nej, jag kan själv. (No, I can manage.)
Vill du ha sällskap ikväll? (Would you like some company tonight?)
Nej, jag vill vara själv. (No, I want to be by myself.)
Does that help?
"sig" is an object. Själv(a) emphasises the subject. English merges both of these concepts into all of the self-words.
Han äter det själv. = He eats it himself. (Object is "det". "Själv" emphasises that it was him and no one else.)
Han äter sig (själv). = He eats himself. (Object is "sig" - indicating that the subject and the object are the same person. Själv is commonly used for emphasis.)
I see that you're learning German as well and it's very similar, so the German translations for these sentences are:
Er isst es selbst/selber. Er isst sich (selbst/selber).
själv(a) = selbst/selber sig = sich
Could someone else please explain? I am finding it difficult to understand the other two explanations as I wrote something similar to George. I wrote "De gör det för sina själva". I understand that I should have omitted "för" but I don't understand why the rest of it is wrong, i.e. "sina själva" or "sin själva". Maybe if the explanations were worded differently I could understand them better.