Lawn (weeds) in rental house a problem

Hello. Can anyone give me some suggestions. I am about to move into a rental house that has a large backyard that I would say is about 90% weeds and 10% grass. I have a small dog with fluffy hair who gets covered in all kinds of sticky, hideous weeds when he goes on that "lawn." I would like to do something to kill the weeds and encourage lawn to grow. There is no sprinkler system, so I would have to water by hand or a sprinker on the hose. I don't want to use anything toxic because of my dog. I live in San Luis Obispo, CA. Any suggestions would be much appreciated. Thanks so much.

The soil environment is such that it is more accomidating for the weeds than the grass. Change that.

Fertilize for grass. Mow high and frequently. Water infrequently.