I generally use a small slotted Whia screwdriver or a similar one. Wedge the blade between the spring coils so it grabs it. Go in at an angle and get the spring over the nub on the bottom of the side frame. Your next motion. You want to put a bit of downward pressure to compress the spring and push it inward with your finger. With any luck it will rest on the 2 dimples. When your in. Just slide the screwdriver back and move on to the next one. The other 2 should go easier seeing the one spring will hold everything else in position.
Ditto on the thread or even dental floss so you don’t lose any of the springs. For disassembly. I do it inside a clear plastic bag to catch flying springs. If you do lose a spring. They are available from MTH Parts.