No you can not just use wpn824 (wireless access point router) to connect anything that are not have the wireless capability.
Yes you can just press print in your laptop.. as long as the printer cable is connected to the laptop.
to make a wireless connection, your laptop must have a wireless adaptor (most of them already have internally)
to make your printer work wirelessly, you need a wireless capable printer OR you must have a wireless print server.
I'm considering purchasing this <a href="http://reviews.cnet.com/Netgear_WPN824_router/4014-3319_7-31312124.html?tag=bc">Netgear WPN824 router</a> and I was wondering if I could use it with one printer. Would I need to buy some other wi-fi thing or could I just press print on the laptop and it would work?