Need to wash that pesky corset? Cover the stained/discolored spots with a baking soda paste, then wash it down with vinegar for some hot bubbly action. Use an old toothbrush to gently scrub, then hand wash it thoroughly. Use an old towel to absorb water but don't ring or squeeze the corset. (thanks to Starlit Creations for reminding me about this tip)
Now hang that baby up. My preferred method is to use the same hooks you use to hang up your shower curtain. Metal is fine so long as there's no rust on them, otherwise use plastic. Put one through the last grommet on the top and bottom of each side of your corset (assuming you took off the lacing)*, then hook over the shower bar. Remember to move the bar back a little bit so the water doesn't drip on to the floor. Unless you have a crazy thick fabric it should be dry overnight.
*Personally I replace the lacing/cording every time I wash my corsets. However I also wear a corset sock so mine don't get dirty too quickly. What's a corset sock? Basically it's a cotton tube that you put on before your corset to absorb sweat and make the corset a little more comfortable. If you don't have the time to make one or the money to buy one, just get a tight fitting cotton tank top. Put it on, then your corset, then cut off the shoulder parts that stick up (or don't if something will be covering up that bit).