The actual creation and maintenance of a Coinbase account is free of charge.
Fees are charged for specific actions on the platform. There is typically a service fee ranging from 1.49% to 4% depending on the type of payment method selected (available options are bank transfer, credit card or PayPal) and the transaction volume.
Prior to making a purchase, Coinbase specifies how much they will be taking away as fees in an effort to be transparent.
Transferring cryptocurrency from Coinbase accounts to software or hardware wallets do not incur a fee but will hold a specific amount to ensure the transfer is processed on the appropriate blockchain.