It costs a small amount of coins to enter each solitaire level. You can also enter a level for a free ticket, which can be won in timed events or received as a daily reward. In case you use a ticket to enter a level, you'll need fewer coins for it.
Don't worry: if you successfully complete a level, you will receive more coins than you paid to enter. You'll also get extra coins if you finish a level without using all the cards in your deck, or if you win a level with a bet on it. Good luck!