I would guess the RequestDispatcher is what you're looking for - it's the closest thing towards having one servlet "invoke" another (i.e. pass request handling to another). There's no way (indeed there is no need) to invoke a servlet instance directly. Please clarify for further advice.
Charles Lyons (SCJP 1.4, April 2003; SCJP 5, Dec 2006; SCWCD 1.4b, April 2004)
Author of OCEJWCD Study Companion for Oracle Exam 1Z0-899 (ISBN 0955160340 / AmazonAmazon UK )
Please bear in mind, though, that getting one servlet to call another is like going out into the street and knocking on your own front door just to ask someone to pass the salt.
As a reality check, ask yourself what the servlet you are calling actually does, and if you can make that behaviour available to both servlets by something like s simple method call.