As of July 10th, the comet appears as a bright, round fuzzball roughly 8' across, with little hint of a tail. It will probably peak in brightness shortly after July 14th, when it comes nearest to Earth. Then it should fade gradually until perihelion, its closest approach to the Sun, on August 10th. But it will be disappearing into the evening twilight by the end of July.
Comet LINEAR makes two close approaches to bright deep-sky objects, which should yield excellent photo-opportunities. On the night of July 13-14, people in Asia will see it pass just 12' from the beautiful lenticular galaxy NGC 5866, sometimes called Messier 102. And on July 22-23, for observers in Europe, it pases 22' from Messier 3, one of the sky's brightest globular star clusters.
See Seiichi Yoshida's website for more information on Comet LINEAR. The Harvard-Smithsonian Center for Astrophysics publishes the comet's orbital elements and recent magnitude estimates. And the Jet Propulsion Laboratory helps you visualize the orbit in three dimensions.