“How do you get out of bed with a slipped disc?”

First suck your tummy muscles all the way in without holding your breath. If done correctly your chest will be sticking all the way out. Push yourself on to your side until your you are sitting on the side of the bed. Once feet are firmly flat on floor you must avoid leaning forward. Double check your tummy is sucked all the way in and chest remains all the way out until you are completely standing. You must use your leg and butt muscles only while looking up at the ceiling. Important not to lean your torso forward almost as if you are doing a perfect squat in a gym with a weight belt pulling your tummy all the way in. Do not hold your breath but focus on holding tummy in while standing.

It varies slightly. Easier to answer if we could have a conversation about how you slipped your disc.

Roll on your side with knees bent. Push up into a sitting position and when there support yourself with your arms until the spasms begin to subside. Use a cane or chair to support you while standing and slowly come to an upright position. FYI, if you were advised to use a heating pad it will have a negative affect. An inflamed disc is just that, hot and swollen. Ice packs covered with a towel and applied 15 minutes 3-4 times a day will be more helpful. You wouldn't put heat on a sprained ankle so why an injured back. Hot Epsom salt baths or hot shower will help relieve soreness and relax muscles because it is diffuse heat and not direct like a pad.

Lay on the side that's least affected with pain and push yourself up sideways with your arms

There is no correct way on this. It all depends on where its slipped and the severity. I suggest strengthening your core/ab muscles so you are using your core to sit up. You can also roll onto your side near the edge of the bed and push yourself up.