Let's start with the standard scenario for the relativity of simultaneity:
The starting point of everything is the postulate that the speed of light does not depend on the frame of reference.
Now consider a train station. On one end of the platform, there are stairs, while on the other end there's just a wall. Exactly in the middle of the platform is a lamp. When the lamp is lit, the light moves away from the lamp with light speed. Since the lamp is in the middle of the platform, it reaches the stairs and the wall at the same time. Nothing unusual yet.
However, now consider a train going through the train station, entering from the side of the wall. It doesn't stop, but just goes through with constant speed. And it does so just as the lamp is lit. For an observer in the train, the light again travels at the speed of light. But the platform is also moving as well. Therefore the light has to play catch-up with the wall, while the stairs are approaching. Therefore obviously the light will arrive at the stairs before it will arrive at the wall.
Therefore the events "the light reaches the stairs" and "the light reaches the wall", which happen at the same time for the observer on the platform, happen at a different time for the observer in the train.
In particular, if the observer in the train has a device that can send FTL signals, he can use that to send a message from besides the stairs when the light arrives there, and have it received later besides the wall when the light reaches the wall.
Now let's add another train going in the opposite direction. Of course the same argumentation applies also for that other train, but since it is going in the other direction, it's now the stairs that the light has to play catch-up with, while the wall is approaching. An observer in that train will therefore find that the light reaches the wall before it reaches the stairs.
Now consider again the FTL signal above. That FTL signal was sent when the light reached the stairs, and was received when the light reached the wall. But for this observer, the light reached the stairs after it reached the wall. Therefore the FTL message was sent to the past.
And of course, if that observer has a FTL device, too, he can send a signal from the wall event to the stairs event. Indeed, if he sends a bit faster, he can even send after the light reached the wall, and have it arrive before the light reached the staircase. Which allows him to react to whatever was sent with the first FTL signal.
But if the signal arrives on the stairs before the light does, it especially means it arrives before the original signal was sent from there. So we have a manifest causal loop, as the observer in the first train could now react to the response to his message before he sends the message.
To make that into a full-blown time travel, you only have to have a person instead of a message do the two FTL travels, and have the person change trains (which needs only ordinary sub-light acceleration). Obviously the time is too short to do that with the trains, but with spaceships and interstellar distances, that would be completely doable.