FIRST, here’s wikipedia:
The 1997 altered version of Star Wars depicts Greedo firing a shot at Han Solo shortly before Han responds in kind. In the original 1977 version, Han is the only one to shoot.
In the 2004 DVD release, the disputed scene was altered again. In this version, Greedo still shoots before Han does and still misses at close range, but the timing is altered so the shots are fired at nearly the same time and to depict Han “dodging” the shot (digital manipulation is used to “lean” the character to one side).
You can see that here, in this YouTube clip. This clip has the added advantage of presenting the entire scene, so you can see Han readying his pistol below the table. It also goes into super slo-mo, so you can clearly see the two shots.
Bill Whittle has a definitive discussion on the topic. The whole thing is entertaining, but includes, at about 1:30, the original scene. The scene is short – Han says “I’ll bet you have” [been looking forward to this for a long time] and as the camera still focuses on him, a blast is fired in the lower half of the screen – approximating a shot fired below the table, and toward the left side of the screen – just where Han’s hand was shown readying the gun.
You can see, between the two versions, that the altered version adds a broad view before the shot(s) are fired, so the the two shots can be easily illustrated (yes, like in a coloring book.) Check out the “lean” of Han – yes, it looks very…. convenient.