>>I've been asked to write a class library in C# which will open a connection to an SQL server and do some various updates, deletes, inserts, and so forth in some various tables that exist in two databases on that server

Bonnie Berent has an excellent blog on this subject.
http://geek-goddess-bonnie.blogspot.com/2009_10_01_archive.html
I've used some of its ideas in creating a data access framework that's the basis of several successful C# apps.
You'll probably want to take it further, but it's a great starting point.