You are looking at an antique Sargent padlock with original push key. Simply push and turn. It has Pat. 1912 stamped on the bottom. - eBay
By pushing up he means that when you insert the key, you need to push the key and keyhole up into the lock. It is then the lock itself that rotates while the key remains in the relatively same position in relation to the hasp.
This lock sold for $20.12 (Plus $11 shipping) here after first being listed at $24.99 (Plus $11 shipping) but received no bids at that price.