Preface:
CC -> Carbon Copy -> Everyone can see all email addresses
BCC -> Blind Carbon Copy -> Everyone can see only his/her email address and the To email address
Sending BCC with Mail:
1. Create a new email (Cmd + N)
2. Compose your Subject and Message Body
3. Show BCC field (Option + Cmd + B)
4. Write an email address into the To: field (hint: use the address you're sending from -> your email)
4a. Drag and Drop a Group from the left sidebar of Contacts.app into the BCC field (hint: Create a Group like Family if you don't already have one. If a contact has more than one email, you can select which one to use by Edit > Edit Distribution List)
5. Send the email
4b. Without using Contacts.app, open TextEdit and write down or copy email addresses formatted like this:
Code:
example@example.com
example2@example.com
example3@example.com, example4@example.com
"Mrs Ex Ample"<example5@example.com>, "Mr Ex Ample"<example6@example.com>
Select all wanted addresses and Copy and Paste them into BCC. Blank lines don't matter. If all went well, valid addresses are getting colored by Mail.app
There you've got your basic mailing, though this won't let you use custom text for each recipient. To get this done, you'd need to learn how to create and send a newsletter. Vanilla Mail.app can't do this and you might better choose a web-based service to get this done. Some of them let you send bulk email for free to a limited number of recipients (around 100). That's probably not as fast to learn as you're asking for if you're doing this for the first time.
Happy Birthday to your mother...