As Thaddeus correctly states, The Avengers doesn't explain how Thor got to Earth, except making brief references to “dark magic”. Since then, a prelude comic to Thor 2 was published which explains this in more depth.
Thaddeus’ answer was written in June 2012. In June 2013, Marvel published a comic called Thor: The Dark World Prelude. It spans the gap between Thor and (presumably) Thor: The Dark World, covering events of The Avengers (which occurs between the two).
This comic explores the destruction of the Bifrost, and the effects that has on the nine realms, and Asgard's ability to keep the peace. Here’s a page from the first issue, which mostly confirms Thaddeus’ theory:
Odin uses his staff (and dark magic) to send Thor to Earth (called Midgard above), after witnessing Loki’s plans and realising that humans had the Tesseract.
In the second issue, Thor and Heimdall use the power of the Tesseract to rebuild the Bifrost. This allows them to restore peace to the nine realms, and presumably sets the scene for Thor’s return to Earth in Thor: The Dark World, The Avengers 2, et al.