It heads for the bar then the hors d'ouvre table before mingling with the other bills and trying to pick up a few earmarks.
(I know this isn't what you wanted but, I couldn't resist.)
Usually, a bill goes to a committee to get marked up with any earmarks used to buy votes and any changes deemed necessary. It is then presented to the Congress, one house at a time, and voted on. After passing in both houses of congress, usually in two different versions, a joint conference committee meets to work out the final wording. The final bill is then voted on. If it passes both houses of congress, it is sent to the president for signature and becomes law.