How can a new writer get her first book published??

Answer 1

Get a list of agents who represent books in your genre (The Writer's Market is an excellent resource for this) and send the first three chapters of the book (hard copy, not e-mail or disk) to everyone on the list. Then start your second book while you wait so see if anyone will get back to you.

If your book is a non-fiction book targeted to a niche audience, skip the agent and contact publishers that publish for that niche directly. Visit their web sites to find out how they want to be contacted.