I'm aware that there are several toolkits, but what AJAX does seems pretty simple, just load php file with a post / get request, and I have done this with copy and pasted basic ajax code, but there are toolkits like mootools and sajax.

What do these improve on? What do they feature?

Basically, every major browser have slight differences in how they handle things.

For example, when you click on an element in the page, firefox send the reference to the clicked element as "this", but IE sends the event itself, as the origin of the click, and you have to check different properties of the event to find the HTML element.

There are numerous things like that, and often, they add useful functions (like iterators and enumerators) to primitives that had no support for those.

It's not that you cannot live without them, it's just that they make your life simpler.

Prototype is the main one I use: http://www.prototypejs.org/

There is plenty of documentation and examples on the site but you might do some googling for 'prototype js ajax', you should come up w/ some tutorials.

JQuery is popular too: http://jquery.com/

Again, they have documentation and tutorials on their site but you may find it helpful to google for additional resources.

One more question regarding AJAX.

I have used AJAX on one of my sites just to play about with it, but is there another way of using PHP/AJAX without having to call an external php file or is that the only way?

Ajax is nothing more than an acronym to create a request to the server from a fragment of javascript.
So, you could have an asp script, or jsp, or cgi on the other end. Even a static xml or html file if you want.

But yes, you need something on the other end.
If you are talking about the effects that you find in libraries like mooFx, or scriptaculous for example, no.
Those are pure javascript/DOM scripting, and you don't need no server to apply those.

So, what do these toolkits feature? Just give an example of what one could do then I'm sorted =)

They all do the same thing, simplify the AJAX and effect application via a specific syntax.
I personally use prototype + scriptaculous, but they don't offer anything else than yahoo toolkit, dojo, moo, jquery offer too.
It's just about a syntax, not functionalities.

And for what they provide, take a look at their demo pages, and do your choice there.

Thank you