Let me first qualify this post by saying that I actually do day trade.
Day trading generally refers to the activity of getting in & out of stocks within a day, so you hold no positions overnight.
There are some day traders that scalp for just a few cents. This is not the domain where the retail trader can play because of the fees. For the retail trader, I'd say you need to be looking for moves a minimum of 10c. Which is the area I play.
The brokers mentioned - Ameritrade & ETrade would be terrible for the day trader. With Interactive Brokers, I pay half a cent per share to trade. So a 1000 share trade costs me $5. Tradestation costs me one cent per share. Both have pretty good trade execution.
I trade 1-5000 shares at a time generally speaking and I look to lock in a move of 10c minimum but sometimes I sratch (break even) and sometimes lose a few cents. I rarely lose more than a few cents because I trade based on analysing buying/selling pressure and jumping on momentum. Generally speaking, trades move into profit within a few seconds of entering or I get out.
To day trade, you need a minimum of $25k in your trading account - that's a legal requirement. It is better to start off with $30K. With a $30K account, you can actually buy up to $120K in stocks to day trade. This is important because if your stock price is $60 and you want to buy 1000, you couldn't do that with just the $30K. If you aren't buying stocks in the 1000's, you won't be making good money from a 25c trade.
Now - you do not do this with penny stocks. Generally speaking, NASDAQ stocks in the range of $20-$80 dollars are what I trade. I also don't generally trade any stock who's volume is less than 500,000 shares a day. There are 2 problems with penny stocks. First of all, the volume is too low, so when you want to buy/sell, there often isn't anyone to take the other side of your trade at a decent price, so you'll suffer from 'slippage' on your entries and exits. The second problem is the fact that a 30c stock is not going to make a $1 move. It makes no sense to trade at that level because you would have to buy huge quantities of stocks and the liquidity is just not there to get in & out without the price slipping.