Two viewings of the movie and discussions with six other viewers failed to uncover anybody who claimed to understand Third Person. I suspect that a third viewing would have led me to a pretty complete understanding, but Third Person is nowhere near good enough to sit through three times.
But I can give you a few hints that might help you get through it with less bewilderment than the seven of us suffered.
First, keep in mind the possibility that the woman Adrien Brody is so unjustifiably pursuing may be lying in just about everything she says. That story is actually fairly straightforward and could have made a much better movie than Third Person if it had been given an entire feature and not been continually interrupted by misleading parallels and contrasts with the Mila Kunis plot and the Liam Neeson plot.
Writer-director Paul Haggis interweaves his three stories as he did the various plots of Crash in 2005, but this time he does very little to unify his material, except for recurrent themes of love and trust, which some expository material near the end suggests are the themes of the whole shebang.
Ostentatious cuts from one woman lifting her top up and off to another woman pulling her top on and down ought to have some kind of meaning, but seem to be mere segues. And the frequent shots of water, in forms from drinking to swimming pools, clearly link elements of various plots but don't develop any ideas.
Perhaps more serious, none of the characters are either very interesting or very sympathetic; what we can't figure out, we have no great curiosity to know. Third Person has an impressive cast, but they aren't doing much of anything.