AEM 6.1 introduced new CSRF protections for Servlets. If you're using OOTB AEM jQuery, this is mostly handled for you. I want to cover the use case for not using jquery or the granite.csrf.standalone ClientLib.
I've been making it a point to reduce my dependency on jQuery. With an AEM author, you'll never get 100% away from it, but it's possible to do on publish if you're doing typical WCM type sites. Also, with my current project, we are keeping the site as dependency free as humanly possible.
The trick is to send an async XHR request to the token endpoint (/libs/granite/csrf/token.json), pass that token on to your servlet as a header property called "CSRF-Token".
Below you see a fairly basic Sightly Component. Comments are inline.
And a a simple servlet to return the information back...