Start with reading this: http://net.tutsplus.com/tutorials/javascript-ajax/5-ways-to-make-ajax-calls-with-jquery/
Assuming you already know programming, start with php_enhanced_en.chm open on your desktop. (PHP is a trivial language - you don't need to "learn" it.) Search the web for ajax tutorial - there are hundreds of good ones. (The concept is also trivial.) If you don't know programming, learn that first. You're not going to learn any particular programming technique without knowing programming. (Stay far away from w3schools. If you want to learn why, go to http://www.w3fools.com. w3schools is a good place to refresh knowledge you already have (so you realize when you're reading one of their errors), but it's not a good site to learn from, since you'd be learning wrong things.
O'Reilly has a good line of PHP and Ajax e-books.. you may want to check it out.. http://shop.oreilly.com/category/ebooks/web-development.do?sortby=bestSellers&sortType=1