You would have to find an online casino that offers the type of slots you would like to play. Check the reviews on the online casinos and slots to decide which ones are genuine. 
When you choose your online slots casino you would be prompted to download the casino software that would make it possible for you to play online slots. Try to find a few online casinos where you could be a regular customer so you will learn about their bonus programs and other promotional offers.
You will have new games, regular bonus announcements and in general a lot of fun. Most of the online slots machines providers work hard to provide continuous entertainment.
The next step would be that you register with the online casino, then you make a deposits if you want to play with real money.
You can use your credit card, online payment services like Moneybookers or PayPal, check and even wire transfer. If you choose credit cards payment, check out with the provider first as some of them do you process gambling accounts.
Now, you are all set to play online slot machine games. Read the instructions and go ahead and play.