Before starting, make sure that the sendmail-devel package is installed
as well as the m4 macro compiler and cyrus-sasl-plain.  Make backups of both
/etc/mail/sendmail.mc and /etc/mail.semdmail.cf.  I prefer to use a .orig
extension to remind myself why they're there, and avoid having them swept
out by a program looking for .bak.

As root, edit sendmail.mc.  You need to understand that dnl means "delete until
newline" and that anything following it is considered a comment.
A line starting with # isn't a comment, although it looks like one.

Find the lines reading like this:

dnl #
dnl # Uncomment and edit the following line if your outgoing mail needs to
dnl # be sent out through an external mail server:
dnl #

and un-comment the next line, so that it looks like this:

define(`SMART_HOST', `relay:your.mail.hub')dnl 

(Replace your.mail.hub with whatever's appropriate.)
Then add the following two lines:

define(`RELAY_MAILER_ARGS', `TCP $h 587')dnl
FEATURE(authinfo)dnl

Save and exit.  Create /etc/mail/authinfo, containing this one line:

AuthInfo:smtp.1and1.com "U:me@example.com" "I:me@example.com" "P:PASSWORD" "M:PLAIN"

making the obvious changes.  Then, still as root, run these three commands:

m4 /etc/mail/sendmail.mc > /etc/mail/sendmail.cf
makemap hash /etc/mail/authinfo < /etc/mail/authinfo
/sbin/service sendmail restart

If you haven't received any error messages, you should now have it working.