Soft boiled eggs have the yolk still liquid.
To achieve that, you need to place them into already boiling water (the eggs cold right out of the fridge) and at sea level, leave them in for 5 1/2 minutes, by the time you get up in elevation (like Colorado Springs at 5,900') it'll take 7 minutes (lower temp of water at boil)
Then as you take them off the heat, immediately rinse them with lots of cold water, then peel.
If you don't do the cold rinse, they will turn hard because of the latent heat.
For hard boiled (and solid core eggs), you can place them even in cold water and bring the water to a boil, leave them for 15 minutes (from cold).