After the stems have gained enough stregnth and the containing pot looks like it's getting too small for the plant, the seedlings are ready to be transplanted!
It's important to plan your grow to progress with a minimum of stresses to the plant -- in addition to light, temperature, humidity, proper transplanting and care of the root system will minimize a potential source of stress for your special friends and allow the move from a seedling pot/cube/tray to it's new home as gently as possible.
Obviously transplanting does not occur in the wild, but neither does such a controlled germination and early vegetative stage, so I look to that as an advantage over natural conditions when it comes time to transplant.
Ready to roll:
It's important to focus on protecting the root system when moving from the small pot to the larger and keeping it intact -- don't be concerned if you see all of the roots tangled up in the form of your pot, once they are in the larger container, they will spread out quickly.
I let my plants get a little dry, so I can gently work the rootball out without needing to run an object around the container to pop it out -- this is very dangerous to the roots and an uncecessary step which could also possibly introduce disease or worse yet damage some roots. In the next step, you'll be watering the plant fully, which is another reason why I let them dry out a bit before transplanting.
It's important to drop the rootball in deep enough into the pot to allow the roots to spread horizontally as well as vertically, here's a good shot of the little gal in her new home:
I make sure my rootball is flush with the level of the current top of the soil in the container, digging a deeper hole if needed. Once in the pot, you gently replace the soil around the seedling, gently patting the soil to regain it's firmness -- my soil mixture contains enough perlite and vermiculite so I am not worried about the soil being too compressed.
I add my usual large-container amount of tap water that has been run through the brita and sat out open for a few days to allow any contaminants to dissipate and we are all done.
With transplantation complete, I continue to have them on 24-hour light to maintain the schedule they were on -- changing lighting patterns soon after transplanting is not advised, it's a good idea to let everyone stabilize before moving on.