(This question has been answered offline enough times that I thought
it would be worthwhile to include it here.  The FAQ is distributed
widely enough that people may happen upon it through non-Usenet
channels.)

In order to access sci.astro (or other astronomy newsgroups), you need
an internet service provider (ISP).  This could be a large commercial
provider, like AOL or Prodigy in the U.S., or a more local one (check
your phonebook under "Computer Networks" or "Internet").  If you're
enrolled at a college or university in the U.S. (or overseas?), talk
to your computer center; many colleges and universities are now
providing free Internet access to students.  If you don't have an ISP,
you'll have to choose one.  If you're interested in reading the
sci.astro* groups, as you search for an ISP, you'll want to ask the
various contenders if they provide access to Usenet and specifically
to the sci. hierarchy.  If they don't, or can't tell you, that's a bad
sign.

If you already have an ISP, you'll have to read their documentation or
talk to their technical help.  Some ISPs provide Usenet access through
a Web browser (like Mosaic, Netscape, or Internet Explorer), others
provide access through a dedicated news reading program like tin, rn,
or GNUS.  There are many different possibilities.