How do I use the "Investor" perk?

You can't invest in any of the stores/fences in the Ragged Flagon. However, if you were to speak to one of the shop owners in the cities (Angela's Aromatics in Solitude, or Warmaiden's in Whiterun for example) you'll get a dialogue option that says "I'd like to make an investment in your store." I believe the main reason you can't invest in the stores in the Ragged Flagon is due to the fact that:

Upon completing the Thieves' Guild missions, the main fence in the bar will have around 4000 gold to barter with, making investing unnecessary.

You can invest in any that have the dialogue, annd ups their amount of money by (your) 500g. There is a bug that turns your investment in lucan valerias at riverwood trader from 500 into 10k.