How to execute Apex from Custom button or Javascript ? Give Example.

It is possible using Ajax toolkiit.

1	global class myClass {

2	webService static Id makeContact (String lastName, Account a) {

3	Contact c = new Contact(LastName = lastName, AccountId = a.Id);

4	return c.id;

5

}

6

}

we can execute above method from javascript like :

1	{!REQUIRESCRIPT("/soap/ajax/33.0/connection.js")}

2	{!REQUIRESCRIPT("/soap/ajax/33.0/apex.js")}

3	var account = sforce.sObject("Account");

4	var id = sforce.apex.execute("myClass" , "makeContact",

5	{lastName:"Smith", a:account});

To call a webService method with no parameters, use {} as the third parameter for sforce.apex.execute .

Also, you can use the following line to display a popup window with debugging information:
sforce.debug.trace=true;