There is a pattern to express the way of doing things. First comes a verb in the 連用形 form, and after that comes the word 方{かた}. For example:
食べ + 方 → 食べ方 (the way of eating)
読み + 方 → 読み方 (the way of reading)
Given that the 連用形 of the verb する (to do) is し, it seems reasonable to think of しかた as another example of the same rule:
し + 方 → し方 (the way [of doing] )
However, there's a problem: the kanji spelling for the word しかた is 仕方, but the right kanji for the verb する is 為, and not 仕 (the word is spelled in hiragana virtually always).
For this reason, I'm not so sure whether 仕方 is an actual instance of the aforementioned rule or not. Which is the case? Maybe there's an etymological relationship between the pattern and the word 仕方, but it eventually became a word in its own right?