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

It is possible using Ajax Toolkiit.

global class myClass {
webService static Id makeContact (String lastName, Account a) {
Contact c = new Contact(LastName = lastName, AccountId = a.Id);
return c.id;
}
}

we can execute above method from javascript like :

{!REQUIRESCRIPT("/soap/ajax/33.0/connection.js")}
{!REQUIRESCRIPT("/soap/ajax/33.0/apex.js")}
var account = sforce.sObject("Account");
var id = sforce.apex.execute("myClass" , "makeContact",
{lastName:"Smith", a:account});