Since you are doing same thing every month, you may not need to report to your boss on a formal fashion, e.g. calling a meeting for it.
However, if I were you, I'd stop by his office once a while when he seems not busy. I'd just talk with him for a couple of minutes or sometimes chitchat with him maybe on Friday afternoon (usually people are not busy on Friday afternoon), so that he knows I am doing my work and he knows me as a person.
When I have a question and he instructed me how to handle it, I would send him an email updating him about my action and the result afterwards.
When there is communication about an important issue(again, IMPORTANT issue) between me and other people, I would cc my boss and keep him in the communication loop. So whenever he sees a potential problem through the discussions, he can jump in.
I would ask my boss periodically how he thinks my work and where I can improve further.
I would invite my boss for lunch sometimes, so that we can talk something else besides work. To establish a good and close relationship with your boss is always not a bad thing.
In conclusion, it's very important to keep your boss informed. However, you need to have a good judgment on when to do that.