Doesn't Wireless imply No wires ? my bet is the "Wireless" connection to the laptop is a USB stick. You can still run a USB cable or an HDMI cable from the laptop to a Desktop. The laptop would have to be on for the desktop to access the interweb and the software set to allow multiple connections.
Thats doing it on the cheap anything else would depend upon current and/or upgrade capabilities of the two machines.
Not everythng which can be done should be. While techinically you could slave the desktop off the laptop by using the laptop as a proxy server, unless it was one darn fast laptop, connection would probably be a tad slow for both machines.
Back in the day there use to be a book out showing how to use plain old telephone wire to make a weak link lan using only a single phone line and dial up modem. Ah them were the good old days, sharing 2400 baud modems and Prodigy.
But I digress. Most laptops have a 10/100 mbps ethernet connection built on the board now a days as do most dektops. And wireless routers will also have a 10/100Mbps connection in addition to wireless capability. If the desktop has a USB open (and you don't want to use an ethernet cable to the router) you can get a USB wireless dongle fairly cheap. Most that I have seen will 'fall back' to the fastest speed the router is capable of with older, slower ones being cheaper (54Mbps vs 600Mbps) for example.
Also you are limited by the cable modem download speed to the router which is over ethernet cable( usually Cat 5 (10/100) but sometimes Cat 6 (somtimes it is actually Cat5e 10/100/1000) which supports Gibabits per second. As with any system you are limited by the weakest link.
It is really not all that complicated.
