How does one properly celebrate Janmashtami?
Janmastami celebrations have several components and, depending on where you are, what your means are and how close you are to other devotees you will have to see what you can do. The primary goal is to really meditate on Krishna, especially His appearance, and try to minimize anything that will divert your attention.
Generally, devotees fast until midnight, because Krishna appeared at midnight. During all the extra time saved by not eating, they chant and hear more about Krishna all day. I would suggest reading the Appearance of Lord Krishna sections of Krishna Book and/or the 10th Canto of Srila Prabhupada's translation of the Srimad-Bhagavatam.
At midnight, in all temples, there is a big arati, or gathering, where the devotees worship Krishna with various items (conchshell, incense, ghee lamps, flowers), sing devotional songs, and dance for His pleasure. If you're not near a temple, you can set up a picture of Krishna, offer some special food preparations or even fruit and flowers throughout the day, chant Hare Krishna or play a devotional CD, and then at midnight, honor the food you have been offering all day and then go to bed.
You could watch one of the many videos available from Krishna.com that depict the pastimes of Lord Krishna and His birth.
Sometimes, at the temple, there is an abhisheka (Sanskrit for "sacred bath"). The Deity of the Lord is placed on a platform and bathed by all the devotees in milk, yogurt, fruit juice, honey, and ghee. This may not be possible to do at a private home, but perhaps you can watch one of the live webcams broadcasting from the Alachua or Los Angeles temples. You can find out the exact time from Krishna.com.
So, basically, hear and chant as much as you can, read about Krishna's appearance, and finally, fast until midnight, offering Him nice things all day, and then have a feast at 12:01 AM ;-)