Go to the event page. You can do it from the Dashboard:
Press "Board view". If you don't have this button, that means that you don't have neither a permission to approve members for a specific body, not global permission to approve all members:
Select the body from the bodies list. If you have global permission, it'd display all of the bodies here, otherwise only bodies you can approve participants for:
The applicants list would be updated when you will change the selected body.
You can search for a specific person by name:
Also here you can see how much participants of which type you can send and the deadline for board approval:
Keep in mind that cancelled users would also appear there.
To change the participant type/order/board comment, edit it and then press "Save":
If something would be wrong, you'll see an error on the top of the page (for example, if you've set the participant type but not the order, or you've set participant as envoy (50) when you can only send 30 visitors, or there is already an application with such participant type and order):
If everything was successful, you'll see a green notification at the top of the screen: