The key to analysing a primary source is remembering what it is; it's a source from which we want to get useful historical evidence. But, if it is a primary source, then we must remember that it is completely affected by the time it's produced in. So, the most important thing to think about all the time when analysing primary sources is the author! Of course the content is important, but the author has created this source for a reason, and this is crucial to understanding the source.
So, an appropriate set of steps to take would be; 1) read the source to get a general understanding, 2) discover and think about (and if you can, research) the author - work out nationality, political views, anything you find necessary, 3) re-read/study the source in light of these findings, and try and work out what their purpose is. There is a clear method to analysing sources, but it is not easy, and it is very important to remember that all sources are bias! Every source has strengths and limitations, and no matter what, every source is useful for some reason. Demonstrating that you understand this will show sophistication and set you apart from the rest.