How can one find out if he/she is brainwashed? By brainwashed I mean indoctrinated with some political, religious or other type of propaganda.

I assume that you can't be aware of this, because the lack of that awareness is the point of propaganda - to make you believe that something is true/false etc. But there must be a logical way to determine if you are brainwashed. Like "your" arguments following certain patterns maybe?
As Schroedinger's Cat pointed out, there's no clear dividing line between "brainwashing" and the normal processes of growing up in or assimilating into a culture or social group. Even in the case of deliberate, forced procedures, it can be unclear -- for example, the US military has recruits do drills and engage in synchronized practices that we know to affect thoughts, feelings, and beliefs, but most people wouldn't call that brainwashing. However, you could look into military training practices, as well as techniques used by abusive cults, and see if you've been subjected to those at any point in your life. That might answer your question. 

Another way would be to think about the criteria you would use to describe a thoroughly un-brainwashed person, and work from there. For example, do you believe that you should be able to cite a preponderance of evidence for all of your beliefs? That you should have a clear and volitional explanation for your life choices? You can then work toward those goals, questioning or changing your beliefs as necessary. Be aware that hardly anyone really meets these criteria! We all absorb cultural values and prejudices, use unconscious heuristics to make decisions, and make choices that we rationalize later. But you could certainly work on moving in a more rationalist direction if you want to.