As told in the June 2013 Sky & Telescope, on the morning of June 12th a 6.4-magnitude star in southern Ophiuchus east of Antares will wink out for up to 4 seconds along a track from Oklahoma across northwest Texas, southern New Mexico, and southern Arizona, when it is occulted by the small, faint asteroid 332 Siri.
Looking beyond, here is Steve Preston's pick of the best asteroid occultations worldwide for 2013.
And Preston's master list of asteroid occultation predictions.
To learn about today's asteroid-occultation timing world and to join the party, see Worldwide Asteroidal Occultation Observations and Resources. Video is now the standard method. For information on video recording and precise time extraction, see the "Equipment" heading.
For actual human advice and help, join the International Occultation Timing Association (IOTA) Yahoo discussion group, say hi, and ask for help.
Here are results of past timing campaigns (in the "Results of Observations" box at top).
Free e-book: Chasing the Shadow: The IOTA Occultation Observer’s Manual (the preview page).