Read the label of any cleaner you are contemplating using. Look for one with stainless steel abrasive compounds. Some basic household cleaners can be used to address small, less serious, spoke grime.
Apply the polish to the spokes. For less serious cleaning, wipe them with a cloth. For tougher grime, turn on a buff wheel and touch it lightly to the spoke in the areas that you want cleaned. The wheel is for heavy-duty cleaning only; it's a powerful device that isn't appropriate where elbow grease can be used. The buffer will strip some of the steel off the spokes, but the shine is unmatched.
Angle the spoke at 45 degrees to the buff wheel and pull it lightly away from the wheel. Adjust your speed indicator on the buffer to between 3,600 and 7,500 surface feet per minute (SFPM). A high speed will increase the speed of the results.
Hold on tightly to the spoke as you buff. The machine can project an object extremely fast and far.
Place a burn paste over any burn stains. This is basically a phosphoric acid that then needs to be neutralized with sodium bicarbonate, which will prevent the steel from etching.