I haven't used PhoneGap yet, but they claim that you develop apps with plain old JS, CSS, and HTML.
If that's true, then use the API just like you would from a web page -- with simple AJAX calls.
Here's a working example (using jQuery):
var userID = 1416412;
var pageNum = 1;
var pageSize = 100;
var siteParam = 'stackoverflow';
var appKey = 'Get your own key!';
$.ajax ( {
type: 'GET',
url: 'https://api.stackexchange.com/2.1/users/' + userID
+ '/answers?page=' + pageNum
+ '&pagesize=' + pageSize + '&order=desc&sort=votes'
+ '&site=' + siteParam
+ '&filter=!3u0zcO(lpHVEGuskA&key=' + appKey,
dataType: 'JSON',
cache: true,
success: function (apiJson) {
//-- Provide a closure.
console.log (apiJson);
}
} );
[Get a key][1], it greatly increases your quota and is needed if you want one of the methods that needs authentication.
Reference the API docs and the API “Hello World” codeAPI “Hello World” code.