I have one of those watch and grow indoor bulb gardens with daffodils, crocuses, hyacinth, and tulips. I want to plant them outside. Can I do that? If so, how?

Yes, of course you can. After blooming, the foliage would normally grow for a while to store energy in the bulb for next year's reproductive cycle (i.e. bloom). The typical low light levels indoors make it a rather inefficient process there, but once it's warm enough to set your potted bulbs outdoors, you can do that (assuming the foliage has not completely died off already by that time). Any time they can spend outdoors in good light prior to the foliage dying down is to their benefit.
In any case, whether they were able to photosynthesize outdoors to much of an extent or not, you can plant the bulbs outdoors (providing they are hardy species for your area). They may not have the energy to produce blooms the next spring, and if so will only produce foliage, but they will benefit from being outdoors in normal light conditions and should be able to bloom thereafter.

Thank you! I'm not sure if I will have time to get them outside before the foliage dies. I will keep it in a southern window for the time in between.

Reid, here is a photo of the my Christmas gift. They were doing well indoors on a south facing window. As soon as the freezes stopped I placed them outside and they did even better! I should take a picture of it today. Less than two weeks later, the flowers are enormous and standing tall. Two of them have 5 blooms now! They are welcome color to a drab winter landscape. What a treat!
I have others amaryllis bulbs have naturalized and spread in my yard. They, too were holiday gifts from the past. However, they won't bloom until around April in my zone. Seeing how we had a nice colder than normal winter, I expect a great show of flowers this year.