The most urgent problem a shop can have.
FIRST, CONFIRM IT
Buy something yourself, as a guest, on a phone. Do not rely on a customer's description; reproduce it.
Check whether orders are arriving at all, or arriving but not completing.
IF NO ORDERS AT ALL
Is the site loading? If not, this is a hosting or DNS problem rather than a shop problem. Is checkout returning an error? Check cPanel > Metrics > Errors and the WordPress debug log. Did anything update recently? Plugin and theme updates are the usual cause. Deactivate the most recent one by renaming its folder in File Manager.
IF ORDERS ARRIVE BUT STAY PENDING
The gateway webhook is failing. Verify payments in the gateway dashboard and mark orders manually while you fix it.
IF PAYMENT FAILS AT THE GATEWAY
Check your API keys have not expired and the account is in good standing with the provider.
WHILE IT IS BROKEN
Put a notice on the shop. Customers who try and fail without explanation do not come back; customers told there is a fault usually do.
Open a ticket with the exact error and the time it started.