With Roulette the Roulette rules are basically the same whether you are playing either American or European Roulette. The difference between European and American Roulette is that you will find on the European Roulette wheel there is only one zero as opposed to double zeros on the American Roulette Wheel.
The benefit of playing with fewer zeros means better odds for you the player as opposed to more zeros which makes better odds for the house which is the casino. So it is to your advantage to play European Roulette as opposed to playing American Roulette at an online casino.
Regarding the Roulette wheel you will find that with European Roulette the wheel has 37 numbers --inclusive zero-- and the American Roulette has 38 with the double zero on the wheel. You may quite often find that the house edge for American Roulette is 5.3% as opposed to 2.7% for European Roulette.
When you are playing at an online casino you will find that the rules are the same as a land based casino, but that there are other differences when playing at an online casino. Where the ball will eventually lands in an online casino Roulette wheel is all dependent upon the software which is called the Random Number Generator --RNG--.
With a RNG this piece of software is constantly producing thousands of random numbers each and every second, and those random numbers are extracted when an event occurs such as the roulette wheel been spun--. These numbers are mapped until the end when the ball ends up landing on a number which gives you total randomness and appropriate odds.
Roulette Rules for Placing Bets
You may use the chart below which is basically the same whether playing American or European Roulette as the Roulette Rules for betting are basically the same in Roulette.
American Roulette Inside Bets
American Roulette Outside Bets
Regarding your playing of Roulette for the first time, I would recommend to play the free download version and get a better understanding of the Roulette Rules. It is also to you advantage to fully understand the placing of inside and outside bets prior to playing for real money.
Best of luck to you in playing your favorite game of Roulette whether it may be American Roulette or European Roulette.