Q:

How does Thor get back to Earth in the Marvel comics?

In the comics, Thor is on Earth and the bridge between the two worlds of Asgard and Earth is intact.
I haven't read the comics, but in the movie, the gateway collapses. If that's so, how does Thor get back to Earth to become an Avenger?
Or did the movie mess that up?

A:

The movie does not directly explain how Thor gets to Earth. It is hinted that Odin uses up considerable personal power to get Thor to Midgard and that it may have a time limit.
Here is an interview where the writers and actors talk briefly about it here.
"Loki says, 'How much dark energy did the All-father have to muster to conjure you here?' Tom Hiddleston recalled in a recent interview. "The Bifrost is still down, he can’t just be riding down the rainbow bridge, Heimdall [is gone], it’s all changed since the end of 'Thor' so it’s obviously cost Odin a significant amount to get there," he explained. "I guess he’s been sent down by Odin to go and deal with this crazy cat that is his brother." 
Chris Hemsworth reveals that while the movie doesn't really go into the specific details of Thor's return, his time on Earth is actually limited. "It’s not really explained, but it’s assumed that he can only be there for a window of time. Odin has had to call in some favors from around the realm. And he turns up. That or the bus," he joked. 

As an aside, Mjolnir has always been able to open portals between Asgard and Earth, so I wonder why no one there did their homework and just put the line out there in the script.

A:

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.

A:

The question is a little confusing.  As far as I know, the specific plot that played out in the film Thor didn't occur in the comics, it was largely an original story.  So the particular issue of Thor needing to get to Midgard (i.e. Earth) from Asgard without using Bifrost may not have happened in the comics.
In the film, it's clear that the Bifrost is still not functional.  Loki asks Thor how much "dark energy" Odin had to summon to "conjure" Thor to Earth, but we don't see the process happen.  At the end of the film, Thor returns to Asgard by using the power of the Tesseract (the cube from Captain America).  This conveniently confirms the fate of the Red Skull at the end of Captain America.

In an interview with Empire Magazine about Thor: The Dark World, Director Alan Taylor said:

When the Bifrost was broken at the end of the first film, Odin had to conjure a lot of dark energy and go through a lot of personal sacrifice to try and get his son back to Earth. And it was a one-shot deal. If Thor didn't succeed, without the Tesseract he couldn't have got back again.

The amount of energy Odin expended to get Thor to Asgard was significant, so much so that he couldn't bring Thor back.

