Terry - You could be facing a couple of different problems here.
First you need to know where the WiFi AP (access point) is located nearest to you physically in the building (you could have a few within the building) that is open for your use.
It's possible you could be accessing someone's private AP which by chance has access to the internet but thru a slower connection.
Once you know where it is physically you need to know its name and the settings to correctly setup your system to access it NOTE: this is no different for a PC or a Mac. If the distance is quite great you may want to ask the network folks (the one who manages your network at you house) if the AP could be placed closer to you.
OK, is the unit a 802.11n device? if so you should upgrade your AirPort software to support it if you can. See Apple TN AirPort Extreme Update 2007-004 It will update your Airport firmware to support 802.11n networks. Apple at one point sold this now its free. Make sure all other system updates have been applied as well as needed.
What do you see in the signal strength icon in the menu bar? It should be at least 2/3rd lit. If not you maye too far from the AP or the walls between you and the AP are blocking the signal. It's also possible the Antenna in your system needs repair to double check this take your system closer to the AP does the signal improve? If it does its more likely distance/interference issues.
Things which you can do to improve things on your side is to get an Airport Express Base Station (or other WiFi Router that can act as a WiFi repeater) and set it up as a repeater. Place the Express device at the best location within your unit to access the AP that connects you to the Internet. Once you set it up (very easy setup menu to follow) you can use your Mac to connect to the Express AP acting as a repeater which will connect to the other AP and on to the Internet! I would recommend setting up the Express with WPA or WPA2 so others don't connect to it (As the other connection side is not encrypted your info is still exposed! so don't use your credit cards or other personal info that you don't want others to see). If your U-Verse allows WPA or WPA2 connections by all means do set it up! that way your info will be protected over both WiFi nets (repeater AP and U-Verse AP). Just remember each networks WPA/WPA2 connection will use different passwords & encryption keys.
OK, you setup the repeater and the connection is still not very good (slow or drops out): Just like a building you can build a strong basement but the house on top is just rotten! networking is not much different. So far we worked on the physical WiFi connections and hopefully you have a good and stable WiFi setup as outlined above.
The house in our story here is the TCP/IP connection over the WiFi and wired network at the far end of your location (U-Verse to the Internet). Here is where your efforts can come to a bitter end.
You stated above others have good and fast connections so I'll say your TCP/IP connection should be OK, but... the AP your connected to may have higher traffic than other AP's in the building (if you have multiple AP's). You'll need to talk with the in house network folks to find out if they have too many connections on the AP. If they can see if they can move a few connections around to balance the loading or add another AP. If you still find the connection is slow you may need to talk with the U-verse folks to see if your link needs service or you need to upgrade to the next performance level.