If its like the UK system – you get the bank details of the vendors bank – if like WF, they’ll give you their details when you order and say you’d like to wire the money.
Then you go along to your local branch and say you wish to wire some money. They might ask if it’s international or national – answer as appropriate.
Then you’ll probably get a form to fill in… which you’ll put down your bank details the money is coming from, the details of the account the money is going to, and the amount in what currency your sending. Then there will probably be a box for you to put in a reference number of similar – I put down something that they would recognise as I didn’t have an order number. Like ‘Lord Summerisle – payment for diamond number xxxxxx’ giving the inventory code of the diamond I was buying.
Then you give to the cashier and they’ll process it.