To then call the method via client script you would use the PageMethods object and using the method name as defined in the page class, like PageMethods.ReverseString("some string").
When calling the method, the first <n> parameters in the PageMethods call match the parameters to the class method. In this case its only one parameter, the string to be reversed. Optionally, the next parameter is the callback for success, followed by the callback for failure. Then is the context data, in this case I'm just sending the input control but it can be anything.
If you are curious about what happens next, here is some key info from Fiddler about the HTTP Request and Response.
The request looks like this minus some of the standard http stuff:
And the response:
As you can see, PageMethods are pretty light and extremely easy to implement. I hope this helps save the next person a few minutes of searching.