How can I strengthen a 2.4 GHZ 802.11b wireless signal?
What are the external parameters? What are you attempting to connect - what is the distance, environment, ...?
You can do a search on Goggle for "2.4 ghz wireless 802.11b" and come up with a list of companies selling different products.
Or you can try this Homemade antenna at Wireless.gumph.org
Im in a building and receiving a signal from another apartment, but the signal is only strong enough to enter the closest room. If I take my laptop out of the room, the signal is too poor to maintain a connection. I want to boost that signal so I can bring my laptop in other rooms.
I hope you have permission to use this signal 
Well, if you have permission to use the signal from your next door neighbor, the the easiest way to proceed would to just extend your neighbors LAN to your place with a 10baseT wire or coax cable......