There are a lot of factors that go into the amount of money that you need to start trading penny stocks. Some of those factors include the broker you use, the trading platform you use, the type of penny stock you're interested in and your personal risk tolerance.
You should have at least $500 to start trading penny stocks. This will allow you to buy a decent number of shares without worrying about the commission fees eating up all of your profits. Of course, there are always exceptions to the rule. If you're only interested in buying a few shares of a penny stock, then you could get away with starting with less money. However, we generally don't recommend going below $500 when first starting.