Translation:I did not study yesterday.
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The し is specifically the stem form of the verb "to do", する (する is often added to nouns like べんきょう to turn them into verbs). But yes, the ませんand ませんでした endings can be applied to other verb stems:
食べません--do not/will not eat
食べませんでした--did not eat
飲みません--do not/will not drink
飲みませんでした--did not drink
While we're at it, the polite present affirmative versions are ます and ました
勉強 (べんきょう), "study", by itself is a noun. The addition of する, "to do", makes it into a verb with a literal translation something to the tune of, "to do (the action of) study".
The topic sentence above (going by literal translation rather than grammatically good English) would be, "(As for) Yesterday, (I) didn't do (the action of) study (utmost politeness)".
This occurs quite a lot in Japanese. Another good example is 練習する (れんしゅうする), "to do (the action of) practice". As above, 練習 acts as a noun, with the addition of する making it into a verb.
for everyone who really wants to talk to japanese people, you should learn informal verb tenses before formal (you should use informal with friends)
I don't think I can explain it all in this comment so I would suggest you use "Tae Kim's Guide to Japanese" which is an app that goes through everything from basic to advanced grammar.