first, be acquainted with these moves:
Spring-cancelled aerial (SCA): while falling, use an aerial move of your choice, then FF onto the spring.
Double Jump from spring: If you used up-B, land first. If you end up hitting the spring, double jump immediately after bouncing.
D-air "stall": D-air as soon as you bounce on the spring.
In training mode, set up a grounded spring near a standing character then lagless D-air away. This leaves you with about 2 seconds to do spring-related movements. You can try SCA combos by hitting them with an aerial on your way down, then either following them immediately with a DJ aerial or knocking them upwards with D-air if they're grounded and near the spring.
So for example (and I did this in a real match so I can cite it):
I do a retreating grounded spring>D-air.
My opponent (Pit) started walking towards me and ended up just in front of the spring.
I started a SH F-air towards him. He shielded but towards the end, I shieldpoked the back of his shield.
Instead of landing, I hit the spring and went into instant D-air (hit him upwards since he was on the floor).
D-air got cancelled by spring and I B-air him on my way up.
A more common thing I do is after retreating Spring>D-air, I might do an aerial towards the spring, then 1-3 D-airs on it. Then as the opponent walks towards me, I'll go into HA right after bouncing.