A payment gateway is what lets your website (and your Point of Sale) charge cards. BookRouter supports Square, Authorize.net, and Braintree, all managed from one hub: Settings › Connections.

The hub
Each gateway has its own panel in the Payments rail on the left. Pick a gateway, enter its details, then make it the active gateway — the active gateway is what checkout and the POS use. Only one can be active at a time, and you can switch at any time. The Active gateway indicator at the top-right always shows which one is live (or None).
Square
Connects with a sign-in authorization — no keys to copy (see How do I connect Square?). Options include delay capture (authorize now, capture within six days) and Strong Customer Authentication for EEA/UK sellers.
Authorize.net
Enter your Login ID and Transaction Key from your Authorize.net account, choose the authorization type, and optionally enable CIM (Authorize.net's stored-card vault), which lets you charge a saved card later from the order page.
Braintree
Enter your Braintree Merchant ID, Public Key, and Private Key, then make it active.
Setup is free with no additional platform fees — you pay only your gateway's own processing rates. Not sure which to choose, or need a hand connecting? Use Contact Support on the gateway's panel.