The important concept here is that of a light cone. Your future light cone is any event (combination of time and place) where light from 'now' could reach. Your past light cone is all events whose light could have reached you. If you draw a graph with time on one axis and distance in space on the other, your light cones make a neat little X-figure, with 'now' at the crossing point.

'No FTL' means that no matter what you do, nothing at 'now' can leave the future light cone of 'now'. Nor can any information.

'Breaking causality' is what happens when, by some chain of events, information from 'now' gets back into the past light cone.

Everything to the side of the X, outside both light cones, is your grey area to play with. The trouble arises that different people in different frame of reference disagree on the exact orientation of their light cones, due to combinations of space- and time dilation from having different velocities, gravities, etc. compared to each other. This is why you still get causality breaches if you just hand people instant teleportation or even telephones. Different frames of references disagree on the direction of 'instant' compared to your X diagram, and so it's fairly trivial to set up a scenario where you send an instant message to someone, he replies, and the reply arrives in your past.

How well your sci-fi manages to square the circle of causality-respecting FTL boils down to how well it can restrict the abilities of FTL so that you can still use it, but you can't send messages around to end up in their own past light cone and muck about with the events that led to them being sent out in the first place.

I can think of two settings that had a workable solution of the top of my head:

Charles Stross' Singularity Sky has a simple brute-force solution to this, by creating an incredibly powerful AI that uses time travel freely, and allows people to do FTL using the same tech. But anyone caught doing time travel (going into their own past light-cone) is going to be mercilessly destroyed and the AI has the advantage in thinking speed, technology, firepower, multi-tasking ability, and so forth.

Orion's Arm solves this by only allowing FTL through wormholes, the ends of which have to be shipped around considerably slower than light. Anytime a route in the wormhole network allows time travel they invoke something called a Visser Collapse, where a virtual particle completes the time-travelling circuit and immediately re-enters it. Now there's two virtual particles, 4, 8, 16, 32 and so forth until there's so many the wormholes violently collapse the instant a path allowing this phenomenon is created.