Nonprofit Salesforce Learning Resources (mostly videos, mostly short):

Overview of Salesforce: http://salesforce.acrobat.com/crmnaveng/
(you may need to log into your Salesforce account first)

Overview of the nonprofit starter pack (a little out of date, but still most useful):
http://www.youtube.com/user/SalesforceFoundation#p/c/62F1027976C48D90/18...

Documentation of the NPSP: Salesforce Nonprofit Starter Pack. Though somewhat technical, useful overview of the main components added to standard Salesforce Enterprise.
http://wiki.developerforce.com/index.php/Nonprofit_Starter_Pack

Here is a detailed overview of the main Salesforce elements--Leads, Contacts, Accounts (Organizations) and Opportunities (Donations). Nonprofit users might want to do this after looking at the Nonprofit introductions first: http://salesforce.acrobat.com/salesrepfundamentals
You will need to log into Salesforce first to see this and some of the other trainings. Once there, you can find virtually endless tutorials on general topics here: https://na7.salesforce.com/help/doc/user_ed.jsp?loc=training

Understanding Affiliations: how to flexibly connect individual contacts to organizations:
http://www.youtube.com/user/SalesforceFoundation#p/c/62F1027976C48D90/5/...

Understanding households: how to group individuals in a household shared address:
http://www.youtube.com/user/SalesforceFoundation#p/c/62F1027976C48D90/9/...

Understanding Relationships: how to connect individuals together
http://www.youtube.com/user/SalesforceFoundation#p/c/62F1027976C48D90/6/...

Donations:
Long video from workshop a year ago.
http://www.youtube.com/watch?v=XBVo_rmoQhk&feature=related

Understanding Campaigns:
http://salesforce.acrobat.com/campaign
Another option on campaigns is this introduction to iContact, an email marketing tool. Whether or not you user or plan to use iContact, this intro is helpful: http://videos.icontact.com/videos/ic4sf-03_v03.html

The New Reporting System
http://salesforce.acrobat.com/gettingstartedreportsdashboardseng/

Email Communication with contacts
Salesforce makes it easy to send one-off and pre-formatted messages to contacts from within Salesforce itself.
To send standard messages from a template, you need to create the templates first. Here is a video from iContact.com that applies pretty generally to the process of creating email messaging templates:
http://videos.icontact.com/videos/ic4sf-02b_v03.html

Salesforce also connects to desktop, webmail, and mobile email systems. You can send emails as you do now, and have the emails also become part of the contact, organization, or other Salesforce records. This requires decision-making and configuration in advance, and these tutorials are meant to give you ideas about what is possible:
Start with video lesson on Outlook: http://www.youtube.com/watch?v=Zsbz8VQ0dc4
Whether you use Microsoft Outlook or not, this video gives an idea of your own email can possibly be integrated with Salesforce.
Here is an overview for Gmail and Outlook: http://www.salesforce.com/smallbusinesscenter/faq/email.jsp
Mac Users: Here is an open source project for mail integration: http://code.google.com/p/maildrop/
Some smart phones can also tie into Salesforce. The integrations are not perfect and are not for everyone