Conan Doyle didn't. From The Man with the Twisted Lip's dramatic climax (spoiler alert for those who haven't read it):
“You are the first who have ever heard my story. My father was a schoolmaster in Chesterfield, where I received an excellent education. I travelled in my youth, took to the stage, and finally became a reporter on an evening paper in London. One day my editor wished to have a series of articles upon begging in the metropolis, and I volunteered to supply them. There was the point from which all my adventures started. It was only by trying begging as an amateur that I could get the facts upon which to base my articles. When an actor I had, of course, learned all the secrets of making up, and had been famous in the green-room for my skill. I took advantage now of my attainments. I painted my face, and to make myself as pitiable as possible I made a good scar and fixed one side of my lip in a twist by the aid of a small slip of flesh-coloured plaster. Then with a red head of hair, and an appropriate dress, I took my station in the business part of the city, ostensibly as a match-seller but really as a beggar. For seven hours I plied my trade, and when I returned home in the evening I found to my surprise that I had received no less than 26s. 4d.
“I wrote my articles and thought little more of the matter until, some time later, I backed a bill for a friend and had a writ served upon me for £25. I was at my wit’s end where to get the money, but a sudden idea came to me. I begged a fortnight’s grace from the creditor, asked for a holiday from my employers, and spent the time in begging in the City under my disguise. In ten days I had the money and had paid the debt.
“Well, you can imagine how hard it was to settle down to arduous work at £2 a week when I knew that I could earn as much in a day by smearing my face with a little paint, laying my cap on the ground, and sitting still. It was a long fight between my pride and the money, but the dollars won at last, and I threw up reporting and sat day after day in the corner which I had first chosen, inspiring pity by my ghastly face and filling my pockets with coppers. Only one man knew my secret. He was the keeper of a low den in which I used to lodge in Swandam Lane, where I could every morning emerge as a squalid beggar and in the evenings transform myself into a well-dressed man about town. This fellow, a Lascar, was well paid by me for his rooms, so that I knew that my secret was safe in his possession.
“Well, very soon I found that I was saving considerable sums of money. I do not mean that any beggar in the streets of London could earn £700 a year—which is less than my average takings—but I had exceptional advantages in my power of making up, and also in a facility of repartee, which improved by practice and made me quite a recognised character in the City. All day a stream of pennies, varied by silver, poured in upon me, and it was a very bad day in which I failed to take £2.
“As I grew richer I grew more ambitious, took a house in the country, and eventually married, without anyone having a suspicion as to my real occupation. My dear wife knew that I had business in the City. She little knew what.If one could have earned a great living in London by being an excellent object of pity, other beggars would have used self-mutilation as substitute for our Mr. St. Clair's make-up skills; it must then have been St. Clair's particular rhetorical skills that drew the rent. Perhaps St. Clair is better considered a busking performance artist in a winner-take-all market. But it still seems a pretty unstable equilibrium.