To mark an invoice as "selected for payment", click on the button before the
Number column. This will change the state and change the way the button is
displayed to a checked box.

When done, use the search filter "Selected for payment", and select all the
lines to give access to the Actions menu, in which you can select "Register
payment" to display the Payment wizard.

The selection is cleared when the wizard is displayed, whether the payment is
done or not.