Allow the pool to circulate for 30 minutes after adding chemicals to retest. This should evenly distribute what you added. Be sure to brush in the area where you added chemicals immediately after, especially with solid chemicals. I always brush after adding bleach or acid as well, to eliminate the chance of it settling on the bottom and bleaching or damaging the pool surface.
For sampling, I always test in the same location in the pool, collecting the sample from well below the water's surface. Rinse your sample bottle with pool water a couple times, then hold it upside down, pushing it well below the surface. This traps air in the bottle. Then when you have it in deep, invert to allow it to fill with water from that depth. Another very handy solution to do this without dipping your arm way into the water is to use about a 4-5 foot length of 1/2" ID PVC pipe. Plug one end with your thumb, push the open end deep in the water, remove your thumb allowing the pipe to fill, then put your thumb over the end again and pull the pipe out. Hold it over your sample bottle and let it drain into it.
For sampling, I always test in the same location in the pool, collecting the sample from well below the water's surface. Rinse your sample bottle with pool water a couple times, then hold it upside down, pushing it well below the surface. This traps air in the bottle. Then when you have it in deep, invert to allow it to fill with water from that depth. Another very handy solution to do this without dipping your arm way into the water is to use about a 4-5 foot length of 1/2" ID PVC pipe. Plug one end with your thumb, push the open end deep in the water, remove your thumb allowing the pipe to fill, then put your thumb over the end again and pull the pipe out. Hold it over your sample bottle and let it drain into it.