if there is no zipper, you will have to undo one of the size seams -- on the widest side, pull out the existing foam, use the shape to measure what size you need to replace it, most fabric centers carry foam rubber and will cut to order ... reinsert the new foam and using a curved upholstery needle restitch the seam ... ( that same fabric store should have a wide assortment of needles ).
Put it inside a plastic bag so it will slide in easily
Plastic bag works just tear the bag and pull it out. Another way is to form the foam pad into a "U" and stuff it into the cover. Release it and it should form out.
Murf,. This is a real task. If the foam is one piece it's very hard. Try to put each side in little t a time, and alternate from side to side. As you go, check that your following the piping on the cover. Aloha!
I just redid a few of my couch cushions with new batting. I did the old plastic bag trick. It will slide back in the cover so much easier. It is a chore and I found out you don't necessarily have to remove the bag unless it is a noisy one. I did a wrap with the layers of batting then pushed it into a plastic bag and did the wiggle thing and got it back into its cover and zipped it back up.
I covered cushion with drycleaner bag then new cover slipped on very easily, then pull on drycleaner bag to remove.
I used masking tape to hold the foam in a "u"shape. Then slid it into the cover and then undid the tape working the corners first inside down first . Then the top corners worked down and zipped it up! Hope this helps.