You’re transported back to 1912 armed with no physical items other than some basic period dress. No one knows (except for you) that you’re a time traveller, but you’re free to try and convince anyone who will listen to you. You’re stuck in this time period indefinitely.
You decide you’re going to set about becoming as famous as possible, but you can’t do anything illegal.
How would you go about it?
Compose “Summertime”, “Stormy Weather”, “My Baby just cares for me” and a number of other jazz classics. Become hailed as a musical genius ahead of my time. May take a couple of decades, but that’s fine by me.
Invent the solid body electric guitar. Sorry, Les Paul and Rickenbacker et cie. Beat ya to it.
Write Poirot novels.
Invest in IBM.
Invest heavily in the stock market, particularly in companies that you know still exist today, e.g. Ford Motor Co. Divest from the market in September 1929, right at the peak of the market. Reinvest your funds in the summer of 1932, right at the bottom of the market. Enjoy a huge annualized return on your investment over the course of several decades, and become famous as the one guy who read the stock market perfectly through some of the worst volatility ever.
Invent this.
mmm
100 years?
Join the fight for women’s suffrage. Or does getting arrested for protesting count as illegal?
And then use the profits to:
The downside of this is getting to England in only 2 months.
I’m with this approach. I’d add the predecessors of Chrysler and GM to the investment portfolio, as well as Standard Oil. Then buy radio licenses in the 1920s and TV licenses in the 1940s.
I’d add that if you do this right, you’re going to be famous more for being richer than God than for having read the market perfectly.
Invent fuel injection.
Heck, go ahead and book passage on the RMS Titanic’s voyage of April 10, 1912. But do some prep work before you go: Do your research to learn which parts of the ship avoid immediate damage and are waterlogged last. Book a cabin in this area. Bonus points for locating the cabins certain wealthy and/or powerful individuals are using. When you’re aboard, hoard some life preservers and stake out a lifeboat. When the sinking begins, be that heroic and quick-witted person who saves the lives of [insert historical figures here]! A lifetime of book tours and speaking gigs lies ahead of you 
“Develop” working semi-automatic, full automatic, and suppressed small arms for military use. In particular, make extensive use of manufacturing shortcuts that decrease costs and speed production. License all of these to major manufacturers or even donate them outright to governments. Might also “develop” some heavier weapons along the way. No AFV’s though. In the upcoming 1914 follies, my “creations” should result in even higher body counts than we saw in reality. I’ll go down in history as the evil, bloodthirsty arms merchant responsible for the carnage in the trenches.
Can I do a little research beforehand? Like how to produce Penicillin, plastics, radio/radar systems, etc.
If not, I think I could manage at least a wireless telegraph.
Fortune telling -
I see a diminutive dictator escaping from his island prison, and returning to France.
A Duke will defeat him a few months later.
Me, I’d try to start Disney early. 
In 1912?
There’s a whole mess of physics knowledge I could take back with me and bestow upon the world in 1912. Assuming I had a little bit of time to prepare and brush up on the math behind the theories, I’d probably be able to go down in history as one of the greatest scientists of all time.
Expose Thomas Edison for the amoral hack he is and promote the genius of Nikola Tesla.
Short sell the White Star Line (owner of the Titanic).
