It is very hard to predict when the eggs in the cases you receive will hatch, so, unless you want to follow the steps outlined below, you should release them the day you get them or the next day. Using a needle and thread, pierce the egg case near one end and knot it to attach the thread to the case. Cut the thread so it is about 4 inches long. Take the cases with the thread to the release site. Tie the cases to a stem or twig of the target plant by wrapping the thread around the egg case and the stem a few times, then knot it to hold it in place. It is best to put these lower in the plant where it is shady and they don't get hit by direct sunlight all day.
If you want to be able to see them up close, place the egg cases in a glass jar, a terrarium, or an empty aquarium. Put this container in a warm place where you spend time every day, but not where it receives direct sunlight. Make sure to check it daily until they hatch.
Since the mantids are cannibalistic, it is best to release them shortly after hatching, but if you want to raise a few, keep 3 or 4 in the container and add some objects to give the baby mantids some hiding places. You can feed them aphids and fruit flies or use a butterfly net to collect insects from nearby meadows, though among these will undoubtedly be some other predators which may attack the baby mantids. As they grow they need to be placed in seperate containers or eventually you will have only one.
The Syrphid Fly
This fly usually mimics bees or wasps with the yellow and black banding pattern on its abdomen. The adults feed on nectar and pollen but many of the larvae are predaceous, especially on aphids.