I need step-by-step instructions on how to set up transactional
replication from my local LAN to a server on the Internet in the
following environment:

Server 1. Windows 2000 Server w/ SQL 2000 w/SP3 Standard Edition in an
Active Directory environment.  This server contains the db I want to
replicate.

Server 2: Windows 2003 Standard Edition w/ SQL 2000 w/ SP3.  Not a
member of Active Directory or a domain.

I want the db to updated hourly.  I have successfully generated a
snapshot with no issues but start having issues during
synchronization.  I have tried both push and pull replications.

What kind of issues?

I received error 911.

http://doc.ddart.net/mssql/sql2000/html/trblsql/tr_reslsyserr_1_2d4h.htm

here is a guide how to 
http://www.databasejournal.com/features/mssql/article.php/1438201
http://www.mssqlcity.com/Articles/Replic/SetupTR/SetupTR.htm

Is your problem that the non AD sql server couldnt see the share with
the subscription on it. You chose the location when you set up the
publishers and subscribers; it needs to be shared (network) with
permissions that the SQL Server Agent user on the remote computer
uses.

If that is not the case then how big was the snapshot; can you
distribute it to the server manually and apply it ?