Here's a quick picture guide of the process.
First take a nice potful of seedlings. Some folk advise waiting for two true leaves to grow but my experience is that any time after the cotyledons have fully opened is fine.
Depot the clump and smack it firmly onto the work surface to loosen the soil ball.
Divide the rootball into sucessively smaller portions until you can easily pull individual plants away.
Never hold a plant by the stem. This image shows a murder in progress.
Hold seedling by a cotyledon. Sometimes they break. If plant is expensive, take more care otherwise plant or reject according to how many you want.
Make holes in receiving compost using a cane or similar object.
Guide plant into hole using stick if needed.
The result. Water well and by tomorrow they will all be standing nice and straight.
After about three days I begin to feed mine according to plant requirements. This amounts to scattering chicken manure pellets in the box.