I'm totally new to jQuery and Ajax, and I'm just confused trying to work out whether, if one is using jQuery, one needs the Microsoft Ajax stuff at all?
I'm using ASP.NET MVC (and the last time I did web development it was all about posting the whole page back to the server).
Yes: http://api.jquery.com/category/ajax/.
Chapter 8 of Ajax in Action covers Ajax.
Well, jQuery has a built-in Ajax module, i don't know if that's enough for what you need.
Coincidentally, i am just working on something now involving just this sort of thing!
Put simply, yes, jQuery has functions like get and post which perform HTTP operations via AJAX. These a very easy to use, just look at the examples at http://api.jquery.com/jQuery.get/ and http://api.jquery.com/jQuery.post/
Having not worked with ASP.NET for a while I cannot be sure this is 100% true, but i would assume you can just as easily use jQuery instead of the built in MVC AJAX functions.