(Last updated June 6th.)
Serious comet chasers — people who track faint comets with telescopes and binoculars — have been aware of Comet C/2007 W1 (Boattini) for quite a while. It was forecast to become quite bright for a telescopic comet, 6th or perhaps even 5th magnitude, making it visible without optical aid to skilled observers at dark sites.
For a while, Boattini exceeded its brightness predictions by more than a magnitude. Now it has settled back to its predicted behavior. If it bumps up again — and that's a very big if! — it could become fairly prominent low in the east before dawn in July.
Right now (June 6th) the comet is deep in the southern sky and nearing the Sun, so it's visible only from the Southern Hemisphere. There, people have been seeing it without optical aid under ideal conditions. In late May Boattini was also spotted by many binocular observers in the southern tier of the United States.
As of early June the comet is crossing southern Canis Major. If you're at the latitudes of Australia and New Zealand, start looking for it in late twilight, and continue until the Sun's afterglow has completely disappeared. Click here for a detailed, full-page, printable chart showing the comet's path south of Sirius.
The comet passes directly south of the Sun in mid-June, making it invisible to anybody north of Antarctica.
Boattini will emerge from the Sun's glow around the beginning of July as an early-morning object, low in the east, for observers in both the Northern and Southern Hemispheres. What it will look like then is anybody's guess. Most likely, it will be a pleasant though unspectacular little binocular target. There's a small but significant chance that it will become brighter than any comet since Holmes's spectacular outburst late last year.
And there's an even smaller chance that the comet will disintegrate entirely while it's hidden in the Sun's glow and never be seen again. It wouldn't be the first time that's happened to a comet.