Tuesday night / Wednesday morning will be a total lunar eclipse - it starts a little before 5am (Eastern Daylight Savings Time), totality is around 6:30am, and it ends (theoretically) around 8:30am (more precise times and other time zones at the link above). It is visible in the America,s Australia, and Asia, but not in Europe or Africa; in the Eastern US unfortunately the moon will be setting during the eclipse, so you will not get to see all of it.
If you wish to watch it, I recommend dressing warmer than you think and using bug spray, and start out by going out around a half hour before it's supposed to start (so around 4:30am on the East Coast), watch till you get bored, and repeat every half hour. Binoculars or a low power telescope will enhance the experience, but is not required. If you wish to use a camera, set it on a tripod, open the shutter all the way, and bracket from 1/60s to 5s - use a soft release button or a timer to make sure you don't shake the camera when you trigger it. This APOD photo is an example of what you can do; in it, the Moon moved from bottom to top. Since the Moon will be setting for us and is usually towards the South, it will appear to move downwards, or to the right.