It's very simple, go to one of these shops below and buy a food item in one of the Marapets shops:
Now once you've purchased something, go to your inventory and click on the item, where you should select to USE it. You will be asked which pet you want to feed. You select your pet and click the button at the bottom of the page. Then your pet will be slightly less hungry.
Yes, there's plenty of free food in Marapets:
If you need a thorough guide to help you starting out check here: http://maradanchronicles.wikia.com/wiki/Newbie_Help