My lawn looked very similar to this last year. I would start with a good overseed and fertilizer. If you're not familiar with that search youtube, there are several helpful videos. Then maintain what you have with fertilizer/weed treatments and overseed once again in the late fall. It will take a couple cycles of that to get your lawn nice and lush but it will be worth it.

To loosen up your soil you will want to either have it aerated or if you want to put in some elbow grease you can get one of these: http://www.gardenweasel.com/

I learned most of what I know from this channel: https://www.youtube.com/user/LawnCareMidwest

What you do really depends on where you live, what kind of grass you have, what kinds of grass you want, whether shade is involved, and...whether you're willing to water it as much as 1 inch per week in the hottest heat of summer.

Based on the dramatic difference between the two pictures, and based on grass apparently escaping over the concrete, I'm going to guess you have a Kentucky bluegrass lawn. And I'm going to guess that a tree or building shades the grass in the top picture. KBG is a full-sun type of grass. Where people have a mix of sun and shade, then it would be appropriate to mix a blend of fescues and KBG. Fescue can tolerate shade and remain green, but it tends to thin out over the year(s) and requires reseeding IN THE FALL to stay dense enough to fight off summer weeds.

If this is KBG then overseeding is not necessary. Furthermore, seeding in the spring should be avoided if at all possible. If you had a lot of bare soil, then I might seed now, but you don't. You'll be much better off taking proper care of what you have. Here are some basics:

Water 1 full inch all at one time, once every 2 weeks until the temps get up into the 90s. Then change to once very week. Measure 1 inch using cat food or tuna cans. Time how long it takes your sprinkler to fill the cans. Don't be surprised if it takes hours and hours.

Mulch mow KBG at the mower's highest setting or one notch lower.

Fertilize with synthetic fertilizer on Memorial Day. If you feel the need to do something now, use any organic fertilizer. If you want an inexpensive organic, let us know. Milorganite is fine, otherwise.

Don't be tempted to use weed n feed. If you want to kill weeds, spot spray individual weeds with the appropriate herbicide.

And there's no need to aerate. If you have hard soil, aeration won't work nearly as well as spraying 3 ounces per 1,000 square feet of any clear shampoo.