I’ve just started watching BSG, so I won’t be any help there. SGA, on the other hand, is one of my favorite shows.
In SG1, they end up finding references to Atlantis, and it turns out that it exists, and is in another Galaxy (The Pegasus Galaxy). Now the only gate that can dial out to the Galaxy is on earth, and the only gate that it can dial in the other galaxy is the Atlantis gate. Also, it requires a vast amount of power to dial there, acheived by means of a Zero Point Module (ZPM for 'mericans, Zed-PM for all the rest). A multi-national expidition is arranged, and they are all sent on what very well may be a one-way journey (They only have the one ZPM, and I think all of its energy was depleated by the dialing).
They get there, and discover that the Ancients who inhabited the city were locked in a war with a vampiric race known as the Wraith who feed on people’s lifeforce (for lack of a better term). They were losing badly, so they decide to make it look like the city has been destroyed, and ‘sink’ it. They put up their sheilds to keep the water out, and then dial Earth, where they’d been previously (I don’t remember why they came back to the Pegasus galaxy in the first place, though).
After several thousand years of holding back water, the city’s ZPMs are almost depleated, and the team’s arrival has activated all the city’s vital functions, depleating them even further. It soon becomes clear that if they don’t do something soon, the sheilds will fail. Someone (Probably Rodney McKay, Atlantis’s Smartest Man Ever) discovers that it’s possible to raise the city above water again, thus eliminating the need for the sheilds. They do it at the last minute, and everyone’s saved. For now.
Turns out that the Wraith are still around, though. They keep small colonies of humans on planets in the gate system, and routinely ‘cull’ them for feeding. It turns out that most of the wraith are in hibernation, as their food source isn’t readily available. However, the SGA crew on one of its missions ends up having to attack one of the wraith’s main ships, and thus alerts the Wraith to their presence. Consequently, all the Wraith start waking up. Not a very good thing.
That’s pretty much it for season one: they run around trying to find ZPMs and avoid the wraith. At the end of season one, the wraith come and attack Atlantis. They end up having to detonate a nuclear missle (Courtesy of one of the only technologically advanced civilizations, and love/hate enemies/friends, the Jenai(sp?) above Atlantis, and simultaneously cloak the city to make it look like they self-destructed. Then, one of Earth’s hyperdrive-equipped ships shows up sometime, and the city now has a link to Earth. (It takes 3-weeks for a trip between galaxies, and the ship needs to be about halfway between galaxies to relay a message).
That’s about all the important plot I can think of off the top of my head. I’d reccomend renting Season 1 on DVD if you really want to be caught up. Also, www.gateworld.net is a good resource for all things SG1 and SGA related.