To ship a product for free you can use Flat Rate shipping at the product level.
Flat Rate shipping at the product level can be setup by using the product editor for a small number or products. Or you can use the product import tool for a larger number of products.
Flat Rate Shipping - Product Editor:
- Select Catalog > Products then find the product in question and click on edit
- Once in the Product Editor, Select the Shipping menu and move to the Rate Adjustment Type at the bottom, then select Flat Rate.
- Save the settings so the Shipping Providers will appear at the bottom.
- Place 0.00 in the Rate Adjustment box for the Shipping Methods that will be free. Save any changes made.
NOTE: Leaving the the Rate Adjustment fields blank for the other Shipping Providers is the same as placing Zero (0.00) in them. No Shipping Fees will be added to this Product. 
Flat Rate Shipping - Product Import Tool:
The product import tool under Tools > Data Import > Product Import is used to define free shipping settings at the product level. Use this when you need to set this for a larger number of products.
Custom Shipping Method:
You can also use custom shipping methods to create free shipping. For more info on Custom Shipping Methods, see this article.