No it won't make your connection slow. The wireless router transmits data at 54Mbps which is much, much faster than you can download off the net.
Here's my explanantion of a simple home wireless router in brief:
First purchase a wireless router
D-Link DI-524 IEEE 802.11b/g, 802.3 Wireless Router up to 54Mbps Data Rates 1x10/100M WAN; 4x10/100M LAN
LINKSYS WRT54G IEEE 802.11b/g, 802.3 Wireless-G Broadband Router up to 54Mbps Data Rates 1x10/100M WAN; 4x10/100M LAN
I've used both and these two are very good. D-Link being the cheaper one and Linysys having the name. Now if your laptop has built in wireless adapter, you won't have to get an additional wireless adapter for it. That parts done.
When you get the wireless router, it should come with a CAT5e network cable, power adapter for the router, CD and instructions. On the back of your modem, there should be a CAT5 network cable attached to it. The other end goes into the WAN or Internet port on the back of the wireless router. Usually this port is separated from the other computer ports so it's obvious.
Now you need to connect the desktop PC to the wireless router. Use the supplies cable and attach one end to the NIC from the back of the PC and the other end to Port 1 on the back of the wireless router. Physically, everything is ready to go.
It will auto detect and you should get Internet access on both PCs now. We can talk about file and printer sharing later and security implementation as well. First, you have to get your Internet sharing done.