This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Your users can click on links or form submit buttons, generated by your servlet, that will generate requests to the other servlet.
You can also use response.sendRedirect to suggest that the user's browser make a request to that servlet.
Note: If the other servlet is under a different domain, the user's browser will most likely warn them that the form, link, or redirect is attempting to take them to another domain. This is usually in the form of a gray popup window.