After taking out the queen and syrup (of course) and placing the queen cage in between the frames, I've always just tapped the package box against the ground or hive top a couple of times, then turned it over and dumped the whole thing into the new hive body. I usually take a frame or two out before I do that to give the girls a bit more room to drop down through the frames. If there are clingers that want to stay in the package box, I just lay the box down near the entrance and let them take their own sweet time to move into the hive.
Glad to hear you got your bees. Right now it is raining so be sure you put/keep some syrup on the hive to give them something to eat as the forecast is rainy until the morning and then cooler until about midday Saturday. If you have any questions call me. Linda D. Good luck.