Hi vickiandlarry,
You cannot delete the Contact app from your device, so it is there somewhere....
Check Settings>General>Restrictions, and make sure that Contacts is not set to "Don't Allow Changes"
Do a Spotlight Search (swipe up in the middle of the Home screen) and type in Contacts to see if it may have been accidently put into a folder (the folder name will show up when it finds the listing)
Check each of your Home screens to make sure it is not on one of them - keep swiping to the left to make sure you don't have one sitting out there with just the Contacts on it at the end of the set of Home screens
If all else fails, you can go to Settings>General>Reset, and click on "Reset Home Screen Layout". That will reset all of your icons in their orignal order, and will put the Contacts (along with all of the other Apple iPhone apps) on the first Home screen
Cheers,
GB