For members who want to pay by check (or cash etc) you need to go to the Event Details and from More Options, select Add Attendees.

Then, select the number (and type, if applicable). Select Next. If you've elected to collect information per ticket or order, you'll then be prompted to enter it.
Select a Contact as the Buyer and then indicate whether the Contact has paid (and if so, the payment type) or needs an invoice (and if so, the due date).

Select Add Tickets and your Attendee is added to the list and their payment is recorded.
The details can then be viewed in Transactions and Attendees:

If a Non-Member wishes to pay offline or to be invoiced, then create a Contact for them and then either record their offline payment or send them an invoice.

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