BSA is usually added at 0.5-3% w/v, i.e. for your example of 1%, it will be 1 gm/100 ml of d/water.
The reason BSA (most usually Fraction V BSA - this refers to the purification cycle; for some assays, additional steps such as dialysis, Ig removal etc need to be performed by the user or by Sigma/Merck etc) is used is because its cheap, easily available, and is non-intrusive in most assays, especially Ab based ones.
As a component of coating,blocking and wash buffers, it helps prevent non-specific (weak/van der Waals/charge based/surface effect) protein adhesion to surfaces, so that you don't loose your valuable Abs/enzymes or even cells.