Typically the backrest cover is held on by tack strips inserted into channels. You probably have the two side ones out already if you have the plastic cover on the back off.
You need to remove the headrest, then reach up and pull the tack strip out of the top (it folds under and pushes up). Probably have another at the bottom that just folds over and pushes in. If it's like the W108/W115, this one will be tight.
The bottom cover will be "hog ringed" (not really, different rings) to the pad. Cover is held on by tack strips sewn to the edge, folded over and pushed into channels. You will have to compress the springs and pry the tack strip out of the channel all the way round. Usually stuck a bit, but should come out fairly easily once you get started.
Once the cover is free around the bottom, you will have to pull all the circular steel clips out of fabric flap that folds under the padding. Cover will slide off once you get them all out.
To replace, for the backrest fit cover over, fold upper tack strip under and insert into the clips. Usually not too hard, since the back cover is out. Compress springs and pull cover down and insert bottom tack strip. Will be difficults, usually, as it's tight. Replace rear cover, then compress springs and re-insert side tack strips.
For the bottom cover, place cover in position, making sure the edges of the seat portion are correctly aligned. Sew listing (the fabric flap) to the padding with an uphosterly needle and some cotton string or very heavy thread. Compress springs and re-insert the tack strips all round.
Not a bad job unless the tack strips are in bad condition like they were in my brother's waterloggged car.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!