Learn French: Je sais distinguer les jumelles. - I know how to tell the twins apart.

In French, the verb savoir (to know) already includes the idea of 'knowing how to' do something when it is followed directly by an infinitive verb. You don't need to add a word like comment. The phrase Je sais distinguer completely covers 'I know how to tell apart'.

Is distinguer really the best way to say tell apart?

Yes! While it looks like the formal English word 'distinguish', distinguer is a very common, everyday verb in French used for telling two similar things or people apart.

Doesn't les jumelles mean binoculars?

It means both! Des jumelles is indeed the everyday word for binoculars, but it is also the feminine plural noun for female twins. If the twins were both boys, or a boy and a girl, you would use the masculine plural form, les jumeaux.

Could I use pouvoir and say Je peux distinguer instead?

You could, but the nuance is different. Savoir is used here because telling twins apart is treated as a learned skill or piece of knowledge. If you used pouvoir (Je peux distinguer), it would emphasize your physical ability to do it right at this moment, perhaps because the lighting is good or they are standing close to you.