How Do I Make The Grass Greener On My Side?

Literally. I've been struggling with the grass at my house and full disclosure: I'm a renter, this is my first time being responsible for grass and I don't have a big yard budget.

Also, my back yard and front yard seem to respond differently to water. My back yard is green and lush and I HAVE to mow it once a week or it gets out of control. My front yard, maybe it's a different type of grass, is just trash. Yellow, some spots look burnt, at one point there were literal mushrooms growing in the front.

Some people have told me to water three times per day for ten minutes each, someone else told me to water once for thirty minutes early in the morning, but I don't know the formula, because I've never been responsible for grass before. I know that sounds crazy, but it's true! 33 and I'm battling it out with a lawn for the first time and I want to get it right so that when we buy a house, I can keep up with the Joneses!

How would you go about it?