I have a 12 week old beagle puppy. She doesn't let out a peep when we're home with her or even at night, but when we leave her during the day she barks and howls constantly. We live in an apartment so this is a big problem with neighbors. We are even trying a shock collar right now but it seems like she just gets used to it as I came home for lunch and heard her making a lot of noise again. Any suggestions??

Go to Premier.com and look at the bark collars that use a burst of citronella spray rather than a shock. Hounds can be pretty tough and they are inclined to bark anyway. The citronella just has an unpleasant smell and makes a hissing noise that distracts the dog. While you are on the site, look for some interactive toys like Buster Cubes or Kongs. The puppy has to manipulate these to get to the goodies inside, and it gives him something else to do with his mouth! I have also heard of people hiding the puppy's food all over the house so he can use his nose and "hunt down" his prey. I like these methods because they work with the puppy's instincts instead of trying to turn them off.
You may even need to consider adopting a second pup or older dog, since Beagles are a very social breed and are often hunted in packs.
Let the neighbors know what you are doing, and ask them to tell you which days he barks less so you know what works best. They hopefully will be more understanding when they realize you are trying to fix the problem.

Good idea above to include the neighbors, and even ask for their suggestions if they might have any that could benefit everyone involved. They will be glad that you are not ignoring them, and might be a little more forgiving if you can get them to feel that they are working on the issue with you.

You bought a beagle and hoped it wouldn't bark?be careful with the shock collars I've heard cases of it making the barking worse. A

How often do you walk your dog? You need to ensure you walk your dog a good 30 - 45 minutes before you leave - he'll be too tired to bark. A tired dog is a good dog.