When transplanting seedlings you can’t just pick them up and move them usually. There are techniques and tips to improve their survival after being transferred.
As you are looking for seedlings to transfer you should find ones with two or three true leaves. These have the best chance of surviving transplantation.
When choosing pots for plants you should pick ones that will benefit the way the plants grow. For example plants that will be in pots for a long time like tomatoes and eggplants might have to be put in gallon pots. Many plants can tolerate smaller or shallow pots but you should always do your research.
The best time of day to transplant is during the afternoon or evening. This is because plants lose water during day and close there stomata at night. When you transplant you want to minimize water loss.
While handling small seedlings , handle them by their seed leaves. This is because these leaves will fall off anyways when the plant matures.
When digging a hole for the plant make sure is big enough to fit the roots without bunching them up.
After transplanting water them with lukewarm water. Avoid getting the leaves wet because it can put the plant into shock. Then place the plants in the shade for a few days to minimize water loss.