NASA is expecting a display of at least 80 meteors per hour, and the moon, which will be a crescent, should already have set, so there will be no interference from moonlight.
As a bonus, you should also be able to see four of the planets -- Venus, Saturn and Mars aligned in a triangle above the Western horizon and Mercury near the horizon -- shortly after sunset.
NASA astronomer Bill Cooke is holding a chat for the public on the meteor shower from 3 pm to 4 pm EDT on Thursday afternoon. If you want to participate, go to this Website a few minutes before the chat starts.
Also, here's some background from NASA about the Perseids:
The Perseids have been observed for at least 2,000 years and are associated with the comet Swift-Tuttle. Each year in August, the Earth passes through a cloud of the comet's debris. These bits of ice and dust -- most over 1,000 years old -- burn up in the Earth's atmosphere to create one of the best meteor showers of the year. The Perseids can be seen all over the sky, but the best viewing opportunities will be across the northern hemisphere. Those with sharp eyes will see that the meteors radiate from the direction of the constellation Perseus.
The picture above is of a reflection nebula called NGC 1333 in the constellation Perseus, which will be in the northeast. That's the direction you should look to see the meteor shower. Also from NASA:
Located 1,000 light years from Earth, [NGC 1333] epitomizes the beautiful chaos of a dense group of stars being born. Most of the visible light from the young stars in this region is obscured by the dense, dusty cloud in which they formed. With NASA's Spitzer Space Telescope, scientists can detect the infrared light from these objects, allowing a look through the dust to gain a more detailed understanding of how stars like our sun begin their lives. The young stars in NGC 1333 do not form a single cluster, but are split between two sub-groups. One group is the nebula shown as red in the image. The other group lies where the features shown in yellow and green abound in the densest part of the natal gas cloud. By looking for differences in the disk properties between the two subgroups, scientists hope to find hints of the star and planet formation history of this region.
The knotty yellow-green features located in the lower portion of the image are glowing shock fronts where jets of material, spewed from extremely young embryonic stars, are plowing into the cold, dense gas nearby. The sheer number of separate jets that appear in this region is unprecedented, leading scientists to believe that by stirring up the cold gas, the jets may contribute to the eventual dispersal of the gas cloud, preventing more stars from forming in NGC 1333. In contrast, the upper portion of the image is dominated by the infrared light from warm dust, shown as red.