Vegas World is, at its core, a free to play game. Free Coins can be collected from your Daily Spin, Daily Scratch Tickets from other players, and, if you're lucky, winning at the games. Players playing for free who run out of Coins can always come back the next day and find more Coins waiting for them.
Additional Coins can be collected from Charms and the Gem Machine. Both of those features require Gems, which do generally cost real money.
Buy? What kind of free game is this? (One that wants to stay in business!)
To purchase Gems and a Membership with real money select the Buy Gems option from the drop down menu.