You've just touched on catch 22. All new to the markets start day trading OTC penny stocks. There are many websites which offer paper trading. But non which offer paper day trading I know of.
I use to use Quotetracker and Scottrades free real time data feed years ago. Data was 20 minutes delayed. I have no idea if that is still available. It was good to paper trade with and just what you want.
There are other non broker trading platforms which will offer 2 week free trials, with free level II. Quotetracker is free, but you need a data feed. Those cost money if Scottrade doesn't still offer free data.
I have to say CAUTION with a capital "K" when trading on the OTC, your up against professionals which have no mercy. Basically it's like stepping on a pro football field with no experience. Your odds are you will get hurt bad. But that seems to be the only way to learn.
I have a great deal of experience and at this point in your education, can only say. The main thing to remember is don't get involved with the herd mentality!!!! Buy & Sell with determination, above ask and below bid, when trading a fast moving stock move. Don't wait for a turn around with up trends or down trends. Getting passed by can cost more then, just being first in the next order book line.
The 2nd MOST IMPORTANT thing in the beginning of your learning curve is to preserve enough cash to continue learning. This means greed is very very bad, because greed keeps you in the play until it's too late.
So while you monitor time & sales, level II and bid/ask sizes, to determine patterns, needed to be a successful day trader. Sell quick when profits present. Wanting more, listening to message board herds, and trading what you expect to happen is the road to failure.
There is no such thing as a bad gain, but every loss is bad. What gain you may not get, by selling early cost you nothing.
Much luck, ask questions as you progress. I'll try to help. There is so much for day trading pennies. You will find trying to control emotions the hardest thing to do. But you must to succeed.