You have two options.
1. Picocell (requirements: Existing Internet connection, installation: easy)
As brian mentioned above, AT&T offers a device that connects to your existing Internet connection, called a microcell or picocell. It's basically a very limited-range cellular tower that uses your wired Internet connection as its backhaul. That will solve the call problem, and if you put a WiFi access point on your Internet connection that will solve your data connection problem. AT&T sells them but if you point to your location on a map that shows no coverage sometimes they'll cough one up for free for you.
2. Repeater (requirements: Ability to put an antenna outdoors in an area where signal is available, installation: intermediate)
If you do not have or do not want to use your Internet connection and you have some sort of signal at your house but it just can't penetrate indoors (like I do), what you want in that case is a cell repeater, which are pretty readily available. Most of them will only support HSPA+ at best for AT&T. This is what I use, and if you get a good-quality one it works fine. But you have to have signal somewhere you can put the receiving antenna, and that usually means outdoors so there's some pretty significant wiring involved (think: installing an old-school over-the-air TV antenna).