If you'd like to see a general overview of how permissions work click here.
If you'd like to see how the permissions hierarchy is structured click here.
How to set up an announcements channel
1. Create a new role by clicking on the 'Roles' tab in the Server Settings menu, clicking the '+', and naming the role 'Announcements' (or whatever you want to name it).
2. Assign the 'Announcements' role to the appropriate members by clicking on the 'Members' tab in your Server Settings menu, clicking the '+' next to the appropriate members, and selecting 'Announcements' from the drop down menu.
3. Create your 'Announcements' text or channel by clicking the '+' in your channels list.
4. Name you channel 'Announcements' and click the 'Create' button.
Now you have an 'Announcements' channel.
5. Now, to limit the ability to make announcements in this channel to only members with the 'Announcements' role you need to set the channel permissions. To access the channel settings click on the cog icon next to the channel name.
6. In the Channel Settings menu click on the 'Permissions' tab.
7. Click on the @everyone role and deny the 'Send Messages' permissions by clicking on the check box until you get a red 'X'.
8. Click on the '+' and select the 'Announcements' role.
9. Select the 'Announcements' role to edit the channel permissions for this role. Click the 'Send Messages' check box until you get a green check mark.
Now members with the 'Announcements' role are the only people who are able to send messages in this channel. Everyone else will have read-only access to the channel.