To answer your question:
I know I will have to take what ever the user inputs and place it into a string but how do I implement that string into the parameters of the URL?
You can use the stringWithFormat method of NSString. For example:
NSString *ingredients = @"ingredients";
NSString *query = @"soups";
NSString *page = @"1";
NSString *url = [NSString stringWithFormat:@"http://www.recipepuppy.com/api/?i=%@&q=%@&p=%@",ingredients,query,page];
Before using this URL, it's recommended that you URL encode it.
NSString *encodedURL = [url stringByAddingPercentEscapesUsingEncoding:NSUTF8StringEncoding];
Now that you have your URL, just start a connection to the web (NSURLConnection, AFNetworking, the choice is yours), parse the data returned, and load that into an array to display in the table view.