How can I get greasemonkey to call a function on a page after it loads

One way to call a function in the original page is like this:

location.href = "javascript:void(myFunction());";

It is a bit ugly. There is also the unsafeWindow provided by GreaseMonkey too, but the authors advise against using it.

unsafeWindow.myFunction();

Looks neater but make sure you understand the ramifications. From the manual:

unsafeWindow bypasses Greasemonkey's XPCNativeWrapper-based security model, which exists to make sure that malicious web pages cannot alter objects in such a way as to make greasemonkey scripts (which execute with more privileges than ordinary Javascript running in a web page) do things that their authors or users did not intend. User scripts should therefore avoid calling or in any other way depending on any properties on unsafeWindow - especally if if they are executed for arbitrary web pages, such as those with @include *, where the page authors may have subverted the environment in this way.

In other words, your script elevates the privileges available to the original page script if you use unsafeWindow.

You could try using javascript event listeners.

These execute code on response to object events occurring (such as page load)

For example, to execute code on page load:

window.addEventListener('load', function () 
{
    /* code goes here */
});

Try using: unsafeWindow.myFunction();

More details and info - http://wiki.greasespot.net/UnsafeWindow