I've never had any luck releasing lady beetles, but I know some people have, so I'll give you information that might be helpful to you.
Recently I ordered lady beetles online from Planet Natural. They come in a pouch inside a box that has ventilation holes.
RELEASING LADY BEETLES
(ALSO CALLED LADYBUGS, LADYBIRDS)
It's best to refrigerate them for a while. This keeps them from flying off immediately when you release them. For the same reason, you want to release them in the evening when it's not sunny. I kept mine in the refrigerator for one day, and found very few dead lady beetles when I released them.
I wanted to release lady beetles because I had aphids on my milkweed (not a big infestation though), lace bugs on my New England asters, and unidentified insects eating the leaves of my serviceberries.
I had gotten rain the day I released them, so I didn't need to spray the plants first. It's recommended that you have water on the plants so the lady beetles can drink.
All I had to do was open the pouch and put it over a leaf or branch, and the lady beetles started filing out. They'll also start crawling all over your hand, so if that's going to freak you out figure out a different way. I ordered the smallest bag -- they're sold based on how many square feet you want to cover -- and there were hundreds of them. It took a long time to empty the bag, so I was able to spread them all around my yard. They immediately started exploring their new surroundings. Some even started mating.
They didn't seem especially interested in the aphids. A lot of them were drawn to the rose mallow which hadn't bloomed yet. I don't know why, because I've never seen insects on them other than bumblebees.
The next morning it looked like maybe twenty percent of the lady beetles were still around, and the day after that I saw just a few. Some of the aphids were still there. Maybe I just needed a lot more insects in my yard for them to eat. You can also order a food solution called Wheast that you spread on the plants to keep them around. I tried that a couple years ago and that didn't work either. I'm not trying to discourage you from trying it; I just want you to be prepared if it doesn't go the way you hoped. At the very least, it was an interesting thing to watch, and wherever they went they're still helping to control insect pests. Good luck.