SharePoint provides you with four different permission presets but if you require something different please follow these steps.
1. Login to Sharepoint as a Full Access user.
2. Site Actions > Site Settings.
3. Click on Advance Permissions under Users and Permissions.
4. Click Settings > Permission level.
5. Click on Add a Permission Level.
6. From here you can customize the new permission level.
After this is saved, you will now be able to grant a new permission level to new users or existing users.