Yes, keeping the fur and dander down can be as simple as running a slicker brush over a single-coated dog.
You may have to go a bit further with double-coated dogs. Using a shedding comb, or a Furminator and a good brush.
To get the most hair off the dog when brushing, start at the head and first brush with the hair growth. Then start at the tail and brush against the hair growth and up the legs. Then go back over the dog with the comb in the direction of hair growth.
To use a Furminator toolremember to work in small sections until you and your pet get used to the slight pulling. Work in the direction of hair growth with these tools. There is a full line of Furminator shampoos and conditioners for removing shedding hair. I'm not sure if they work as advertised since a good bath will remove dead hair all by itself.
Which brings us to the next step, a good bath. Don't do this regularly. Once or twice per shedding season is plenty. If you bathe your dog too often he will lose the oils in the coat that make it shiny and healthy.
Use a quality shampoo when bathing. Oatmeal shampoos are usually safe for all breeds and sizes. Use a bottle to mix a small amount of shampoo with water (it's usually a 8:1 ratio but check the bottle for instructions). Use a damp wash cloth to wipe the dog's face with plain water. Bathe the rest of the dog. (Full bathing instructions can be found here.)
So comb, brush and maybe Furminate your dogs daily to keep the hair and dander at a minimum!
Read more about dogs shedding here: How to Control Shedding in Dogs
You may also be interested in: Dog Grooming Tools for Every Dog Owner