In what ways do the Senate and the House of Representatives work together to pass bills into laws?

This really depends on whether the two houses of Congress
tend to agree with each other at a given time or not.  For example, during the first two
years of Pres. Obama's term, the House and Senate have not worked all that well
together.  The House leadership is much more liberal than the Senate and so that causes
problems.  This means that a lot of the time the two houses don't really work
together.

Ideally, the House and Senate leadership can work
together to make sure that they are passing (or at least considering) similar bills.  So
that is one way they can work together.  If they do pass different versions of the same
bill, they also work together in conference committee to get their versions to be
identical.  That is another way they work together.

Of
course, both houses must pass a bill in identical form for it to become a
law.