Hi Sheila,
You can grant users these rights via template security. To access these security settings, go to the Administration Console, navigate to Metadata Management, and in the Templates node, open the template you’d like to grant rights on. In the bottom left-hand corner of that template window, you’ll see a button for Security:

From within the Security window, choose the user or group of users you’re granting rights to. To enable them to set this template, give them the Read Template Access Right:

To enable them to fill in fields, give them the Read, Create, and Edit Field Access Right for those fields:

You can grant these in bulk by selecting the desired fields and hitting Modify. 
You can see more details in the Help Files.