Same way you would in real life.

Face away from the ledge (use right click to orientate Haydee); crouch, and then crouch again.

Chances are you ARE playing the tutorial.

Ahhh, must be using a mouse then. I have trying with trackpad and xbox controller with no luck

Vanessa, Right On! Back it to the ledge as close as possible, then hit crouch again - it does work on Xbox controller after all. Thanks!

The button you'd use to re-orient Haydee on Controller I believe would be the left trigger (the button you use to aim)
Since when you aim, she turns around without moving to face the retical. It's a safe way to flip around without risking fall off ledges.

ok I got that

Further on, how do you jump off a ledge to grab a ledge that's behind you?
I came to a spot with tower platfroms and it seems that I have to jump over to progress. But how do I release a ledge and hold on to a neighbouring or to one that's below/behind me?

A ledge below you, Haydee will automatically grab if you're close enough (so if you drop down a wall to a hole in the wall, she'll grab automatically)
You can't "jump off" a ledge your hanging onto. You can only climb up or let go, so if you're getting into a spot where you feel you need to jump back off a ledge you're hanging from but can't climb up onto, then I believe you're going at the puzzle in the wrong way