How to make money by investing in Bitcoin

There are a few ways to make or lose money by investing in bitcoins. The first thing to understand is that bitcoins are very much like gold or a stock like Apple. It has a value and it could increase or decrease in value at any time. Unlike gold and Apple, bitcoins have been increasing dramatically over the last few years. Early investors have increased their value by a factor of 50x or more. See chart:

By Crookesmoor (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

Bitcoins are also very volatile, its price can move up or down 20% in a few hours. This presents an opportunity for a day-trader to buy and sell bitcoins and turn a profit.
Bitcoins are traded at multiple different exchanges often at significantly different prices. At this time, 1 bitcoin is worth $1,043 at Bitstamp, $975 at BTC-E, and $1,108 at MtGox. That is a 14% spread. If you buy at one exchange and transfer to another exchange to sell at a higher price, money can be made. This is called arbitrage.
If you are an experienced trader you should have no problem making money on bitcoins. If you are a novice, be very cautious.

Strategies for making $ on Bitcoin trading/investing:
1. Buy and hold - they are likely to continue to appreciate over time due to a limited supply and increasing demand. They could also get hacked and become worthless. Bitcoin investing is risky!
2. Buy and sell - short term trades can allow talented traders to make money as the market moves
3. Arbitrage - buying low on one exchange and selling high on another