Check out each link for detailed images and info.
Lap-Band / Gastric Band - This involves putting a band around the upper portion of the stomach to restrict the amount of food you can eat. The band is inflatable and those who have it must receive saline solution fill-ups periodically. It's considered a minimally invasive procedure and is both adjustable and reversible.
Gastric By-pass - This both reduces stomach size and re-routes a segment of stomach and small intestine. The segment containing digestive juices is attached to the food-bearing intestine closer to the large intestine. There are several different kinds of bypasses.
More info here: http://en.wikipedia.org/wiki/Gastric_bypass_surgery
Vertical Sleeve Gastrectomy (VSG) - In this surgery, the size of the stomach is drastically reduced to a sleeve and the remaining portion is removed.
More info here: http://en.wikipedia.org/wiki/Sleeve_gastrectomy
Duoenal Switch (biliopancreatic diversion with duodenal switch (BPD-DS) - This surgery both reduces stomach size and re-routes a substantial portion of the small intestine, creating two separate pathways and one common channel.
More info here: http://en.wikipedia.org/wiki/Duodenal_switch
Info from the Mayo Clinic http://www.mayoclinic.org/bariatric-surgery/types.html