The Passport Problem

So we have some questions that we'll get answered as soon as we get a little less lazy and look it up. As we're planning on leaving our precious homeland well will probably be required to pick up some paper work before we can get out, so we can get back in. But as Bethany's last name is about to become 10 characters longer, we are a bit confused about the proper procedure for getting her up to date visa. Many people have done this before us, so there must be a procedure of some sort for us to follow... Well hopefully.
Anyways, that is one thing yet to figure out before crossing the big blue. That, and I need a visa too. But luckily, because of thousands of years of a male dominate society, I won't be having as many issues with mine as Bethany will. Hopefully...