A few times a day (many people find themselves doing this all the time), turn your earrings so the piercing doesn't heal around them. If you don't turn your earrings, the skin will grow back in around the earrings and you won't be able to get them out. Make a point of doing this at least twice a day. If you do it more often (playing with your new piercing), that's fine. Turning them more is better than turning them less.
Be sure to leave your studs in for at least six weeks (recommendations will vary). If your piercing is having trouble healing - bleeding, crusting (make sure this is clear scabbing fluid and not pus), still painful, etc. - leave your studs in longer and continue to clean the piercings frequently. If your ears are healing well, you can remove the earrings after six weeks. However, continue wearing earrings most days, and stick with studs. Make sure the studs are hypoallergenic if your skin is at all sensitive. Wait a few more weeks, at least, before wearing any dangling earrings or non-hypoallergenic ones (until the piercing is healed even better).
Be aware that once you remove your studs, if you don't wear earrings for awhile, the holes can still close up. The piercings are not entirely healed when you remove the studs. Depending on how often you wear earrings, they can take months or even years to completely heal. (If you rarely wear earrings, then every time you choose to do so you'll be punching through partially-healed openings, are creating the piercing again. Then you start the healing process all over.)
When inserting earrings, hold your earlobe carefully. Don't pull down on it at all. Aim the earring through the hole at a completely straight angle. If it does not work, try changing angles slightly until you can get the earring in. This will depend on the angle at which your ear was pierced. Also, be aware that if you haven't worn earrings in awhile, and your piercings are fairly new, the holes may have closed up. Don't ever try to force an earring through your ear. If it hurts, your ear turns bright red or begins bleeding, stop trying to put the earrings in.
Be aware that while your piercings are new, the holes are larger than they will be (slightly) than when they heal. Don't wear small backings on your earrings; they can actually go inside the piercing and become stuck in your ear. This can cause a lot of problems for you. Should this happen, try to remove it on your own first. Get a cotton ball soaked in peroxide and clean the back of your ear. Then hold your earlobe in one hand and isolate the backing. Use your fingers to try to guide it to the opening of the piercing and remove it. Keep the peroxide on hand. You will need to continue cleaning the wound. Also, because this is painful, the cool peroxide will take away some of the pain. If you cannot remove it fairly quickly, go to the emergency room.
If your ears ever become very red and sore, and begin leaking any non-clear fluid (clear fluid that dries quickly is a sign that the wound is scabbing and nothing to worry about), they are infected. Remove your earrings and see a doctor. You will need to let your piercings heal. You may choose to re-pierce your ears later; however, you cannot rescue this time. Follow your doctor's instructions in the case of infection.
If you follow these guidelines, you are well prepared to care for your pierced ears!