How do fleas help dogs and the other way around?

The relationship between dogs and fleas is a symbiotic relationship, but there is a point of confusion in your question as it implies that all symbiotic relationships are beneficial ones in both directions. The symbiotic relationship between dogs and fleas is classed as a parasitic symbiotic relationship.

Three major classes of symbiotic relationships are mutualism, commensalism, and parasitism. In mutualism, both symbionts (the two partners in any symbiotic relationship) derive benefit from the relationship....

The relationship between dogs and fleas is a symbiotic relationship, but there is a point of confusion in your question as it implies that all symbiotic relationships are beneficial ones in both directions. The symbiotic relationship between dogs and fleas is classed as a parasitic symbiotic relationship.

Three major classes of symbiotic relationships are mutualism, commensalism, and parasitism. In mutualism, both symbionts (the two partners in any symbiotic relationship) derive benefit from the relationship. For example, the flower and the bee both derive benefit from their symbiotic relationship: the bee get an energy source (and makes us honey) and the flower is pollinated. In commensalism, one symbiont benefits from the existence of the other while the other remains unharmed. A classic example of a commensal symbiotic relationship is that between the cow and the egret. The herbivorous cow grazes grasses flushing out insects. The egret follows, eating the insects as they disperse. 

In parsitism, one symbiont feeds off the other leaving the other symbiont damaged or harmed in some tangible way. One example of parasitism that all are familiar with is the parasitic relationship between humans and mosquitoes. They feed off human blood and the human has an unpleasant bite to contend with that can produce varying degrees of severity depending upon individual sensitivities and the contaminants on the mosquito (mosquitoes carry diseases like malaria and dengue fever).

Another example of parasitic symbiosis is the parasitic relationship in your question: the symbiotic relationship between dogs and parasitic fleas. By definition, the parasitic relationship between the dog and flea is a relationship in which benefit derives to one symbiont (the flea) while harm or damage derives to the second symbiont (the dog). The flea sucks the blood of the dog (just like blood-sucking mosquitoes) deriving the benefit of life sustaining nourishment and energy. The dog suffers the bites the flea inflicts and the continuing discomfort since fleas multiply quickly, retain their habitat once they attach to it and are extremely to get rid of even with help from humans.

To answer your question, how do fleas help dogs and dogs help fleas, by definition of their parasitic symbiotic relationship, fleas do not help dogs in any way whatsoever, but dogs (unwittingly and with the result of great discomfort, even disease if the dog is allergic or if the flea is carrying disease, like tapeworm) help fleas by providing a nourishment source and a favorable habitat and breeding ground.