気づかれないように is the structure '[verb-negative-passive] + ように' = 'in such a way that (someone) won't notice me' — purpose/manner with a negative passive inside. 被写体 is the technical photography noun for 'subject' (the thing being photographed). そぉっと is a written rendering of そっと with a drawn-out o, emphasizing the delicate, stealthy quality. 取り出す is a compound verb: 取る + 出す. ファインダー is the English loanword for 'viewfinder.' A precise, cinematic description of a photographer's movements.