Software Engineer at Google
Sounds good! An entry-level position as a software engineer is entirely reasonable with an MS in Computer Science, and the internship will help.
There are a lot of things you can do to help find a job. I agree with Bridget's recommendations. In addition, if you are able to work on any personal projects or Open Source projects, do so! You'll be able to add them to your resume, and talk in more detail about them in interviews. This will build your confidence, give you more hands-on experience, and might help you stand out from a crowd, if the projects happen to be in areas that are of interest to your interviewers.
Also if you can, learn another programming language or two. It is much more valuable to be a "developer" than to be a "Java developer." It usually is much easier to learn additional languages after your first, and can mean that you don't have to pass up a good job just because you don't know the language. For example, I don't know Ruby, but if I wanted to get a job programming in Ruby, I know it wouldn't be hard for me to learn enough to get started, because I have experience quickly picking up new languages.
When looking for companies to apply to, it can seem overwhelming. Try looking at in particular a handful of places where you'd like to live and find out what companies are advertising there. Software engineers are in high demand so you will likely be able to find things. If you are interested in any of the major international software companies (Amazon, Apple, Google, etc), you can probably find out where they have offices on their websites, and that may influence you.
Finally, start interviewing as soon as you can. If you get a job, then that's great, and large companies at least are usually willing to hire people with a start date of "after you have graduated." If you don't get a job right away, and struggle with the interviews, you'll still have time to find out what is going wrong and practice, before you graduate and are under even more pressure to line up a job.