With my 1991 and 1993 I just had to push back a little and pull up on the front like wbrockstar described.
It looks like your car had a replacement carpet installed and the carpet wasn't slit so that the bar retainers can poke thru or the bars were removed completely. They might be there just under the carpet but I can't really tell from the pic. The seat was held in place by the springy metal seat support on the bars.
I found some videos and there's different style retainers depending on the era of Fox body. The pic ALMOST STK posted is for the 1979-89 cars.
On a 1979-89 the underside of the seat should have a section of the thin round spring support on each side that protrudes down in the middle front of each seating area. Those hook onto the 2 small bottom clamp retainers in the floor.
Here's a video for the older style retainers:
Fox body mustang back seat removal - YouTube
The 1990-93 had tubular bars that bolted down on the floor on each side and there were semicircular shapes of the spring support that fit onto the bars.