I have been going to the gym for two months, and I have gained muscle specifically in my biceps. I have seen my mates drinking amino acid tablets. Does this improve muscles? I'm afraid to try them in fear of any side effects.
At your level of training, you don't need to do anything special other than eat properly, and perhaps pay attention to post-workout recovery food. Here is a good survey that covers research on post-workout nutrition, and here are some good guidelines (more) on actual food choices. I'd go more into proper post-workout nutrition, but it's not what your question is about.
About amino-acids, your muscles do use amino acids to build muscle. They're present in all the food that you eat, specifically proteins. They shouldn't harm you at the levels that are suggested by the supplement producers, and they're widely used by strength trainers and bodybuilders. However, excessive use (overdose) could result in neurological symptoms (http://jn.nutrition.org/content/135/6/1557S.full).