I attend the key-signing party at SCaLE every year. Phil Dibowitz usually hosts and has done so for many years. He recommends not to do any actual signing at the party but rather use a worksheet to verify the keys and then follow up at home or in your hotel room) after the party. First each participant reads his/her fingerprint while the rest of us check it off on the list. Then we form a "conga line" to verfy identity with some form of picture ID. Passports are the most trusted form of ID.
There is more information at Phil's website:
https://www.phildev.net/pgp/gpgsigning.html
He also has a program to do some of the heavy lifting:
https://www.phildev.net/pius/
PIUS can be used to manage the party and to follow up after. It is a nice way to process each of the new keys, requiring intervention only to set validation level and it also mails the signed key to the owner automagically.

Hope that helps,
Bert