You are limited in your own Google Apps mail account from sending out more than 500 outbound mail messages. This is enacted by Google to prevent spamming and other types of email abuse. Because of this, you'll need to set up a Group if you wish to send emails to a large amount of people. Here is a quick guide on how you can do that.
In your main mail inbox, you can get to Groups by just selecting that menu option from the top of the window.
Once you are inside Groups, you can go ahead and click "Create a group".
You'll need to name your group. Notice that below this it will automatically create an email as well as a web address for that group.
Go ahead and write a description in for the group. You can also make some choices about the access level here. We're going to just use this to send out messages to people in this example, so we'll choose Announcement-only. Then click on "Create my group".
Now you'll need to invite members to this group. You can add a list of emails in this step. If you have a list of contacts you have exported, you can just copy and paste them in here. Don't forget to write your invitees a message to accept the invitation!
You can now send out messages by adding a new post in the Discussions area.
This is the easiest way to send out mass emails in Google Apps without hitting that 500 sent mail limit. If you need more options we would recommend checking out products like MailChimp from the Google Apps Marketplace which will give you a lot more options and contact management of your mailing lists.