Ask the Mauritians
What better way to get help with your queries than to ask the localsOnline Community
How will I apply only for internet access?
If you already have a telephone line, you can ADSL from Orange like @moricien said. Otherwise you can check Bees (Bharat Telecom) as they provide internet through the electricity line in your house.
You can also get a USB stick that gives you wireless internet; check Emtel's website.
If you give us more information about your internet needs, we may be able to help you more.