First, go to the NASA eclipse site and look up details for the eclipse. Times will be given in UT (universal time), and will need to be converted to local time. For example, here is the timeline for the 1410.08 total lunar eclipse (adding conversion to Pacific time):
P1 Penumbral Eclipse Begins 08:15:33 UT 01:15:33 PDT U1 Partial Eclipse Begins 09:14:48 UT 02:14:48 PDT U2 Total Eclipse Begins 10:25:10 UT 03:25:10 PDT Greatest Eclipse 10:54:36 UT 03:54:36 PDT U3 Total Eclipse Ends 11:24:00 UT 04:24:00 PDT U4 Partial Eclipse Ends 12:34:21 UT 05:34:21 PDT P4 Penumbral Eclipse Ends 13:33:43 UT 06:33:43 PDTSee Space.com's guide to the 1404.14 lunar eclipse for some pretty thorough descriptions of the various stages and what to watch for in each one. However, there's no need to pore over it during the eclipse if you understand the basics yourself. If you won't be spending the whole time outside during the eclipse, at least be sure to come out to take a look at the moon during the several minutes before and after each of the time points listed above, especially U2 and U3.
Some final suggestions:
I'm looking forward to seeing it again at the next lunar eclipse!
Update 1406.12: Added article to newly created eclipse series