There are no specific precautions following gallbladder surgery, allthough your doctor will tell you when you should be able to return to work, or start to lift objects.
The main thing is to try to stay on a very low fat diet as is possible to allow your system to adjust to processing fats in a way it is not used to doing. You can probably find lists or suggestions for fat-free, or low fat foods on several websites, so try googling. You may also find suggestions on gicare.com under 'diets.'
After the GB is removed, the bile which runs out of the liver and into the common bile duct - backing up into the liver along the way - will hopefully do the same thing. The end of the common bile duct has a small muscular opening, and in a 'normal' condition, that muscle retards a large amount of the bile and 'holds it' within the common bile duct and the GB. There is 'leakage' however, and that 'dribble' is normal.
While the bile is in the GB, it is concentrated.
When a section of the intestinal tract signals the biliary system to release the bile, both concentrated and non-concentrated are released - when the GB is present. When the GB is gone, non-concentrated bile is released when the sphincter opens.
What can happen after the surgery - an no one knows why it happens - is the the sphincter (muscular opening) doesn't act like it normally would. It can stay open and when that happens the bile moved directly from the liver to the duodenum, and that 'dumping' can irritate the duodenum causing diarrhea.
It is thought that by slowly re-introducing fat into the diet, it allows the body to readjust with fewer problems.