How do I... call the instance method from javascript

In addition to Solution 1 by Sergey Alexandrovich Kryukov[^], i'd suggest to read this: Create Advanced Web Applications With Object-Oriented Techniques[^]. Author explains the differences between C# instances of classes/structs and JavaScript objects.

Use ajax call for achieving your requirement
in javascript code set a parameter value based on condition and then pass that value to your c# code using ajax
eg.

function myfunc()
{
var url = "/Yourajaxfile.aspx?MethodName=" + value;
$.ajax({
type: "POST",
url: url,
success: function (msg) {


},
Error: function (x, e) {
alert("Error Occured");
}
});
}

then in page load of c# file read value of parameter using querystring and then call methods using if else based on parameter

You can call an instance method with Javascript like following.

<script>
		function CodeBehindMethod(var conditionValue) {
                    if(conditionValue==true)
			alert('<%= GetFirstValue() %>');
                    else
                        alert('<%= GetSecondValue() %>');
		}
	</script>

Code Behind will look like --

public String GetFirstValue()
	{
		return "FirstValue";
	}
public String GetSecondValue()
	{
		return "SecondValue";
	}

In case, I am wrong somewhere, please let me know :)