If you have a lot of moss (usually caused by too much shade leading to weak grass), the moss control is usually ferrous ammonium sulfate sold under a number of trade names. The dead moss needs to be either raked out or taken out with a de-thatcher machine. It is also a great time to rent an aerator (and sometimes a thatcher if you have some moss) to improve the aeration of the turf. When you are done with these chores, buy some new lawn seed to put on the thinner areas after the work is done.
A slow-release fertilizer should be put on the lawn sometime this month. The nutrients will give the lawn some vigor and resistance to summer heat. Normally, the effect should last until mid-June. There are both organic and conventional sources of slow-release nitrogen.
False dandelion (the one with the hairs) or true dandelion and other lawn weeds can be controlled this spring with judicious use of lawn herbicides or aggressive hand pulling. As you probably know, I prefer spot weed spraying to covering the whole lawn with herbicide but I guess it depends on the state of the weeds.
If you need to plant a new lawn or renovate an existing one, get busy! The soil should be worked up and you should have the seed in by the middle of May. Don’t forget to lime and fertilize before you plant. Lime first at about 100 pounds/1000 square feet for the first roto-tilling. Add fertilizer according to instructions on the bag just before the last roto-till.
It is possible to renovate an existing lawn without tilling. You can have a landscape company remove all the existing turf and weeds mechanically. Alternatively, you can spray the grass and weedy areas you are going to replant with a glyphosate type product (one example is Roundup™) prior to replanting. Assuming the weedy grasses are green, they will be controlled by the treatment (though their seeds will not). Remove as much of the dead grass and other weeds before sowing. Often you do not need to till if the lawn is fairly smooth. If, however, the moles have re-engineered your yard, it might be wise to till it and smooth it out before planting.
If you till, make a seed bed that is firm. Rake to shape the lawn, roll the soil after tilling (you can rent a roller) and shaping, then rake grooves into the soil, seed the area and finally roll the planting again. Many people put a thin coating of peat moss over the new lawn to be. If it turns hot right after seeding, it does hold the surface moisture better. Irrigate consistently do bring up a uniform grass stand. Cut it lightly for the first time when the grass is about 2-3 inches high.
Make sure the seedbed is dry enough to support the mower without making ruts. Continue to irrigate throughout the summer if you want a green lawn the entire year. Recent evidence from OSU research indicates that on an established lawn, ¼ to ½ inch of water every second or third day produces a better lawn than an inch or more once a week. See this link for details: catalog.extension.oregonstate.edu/em9311/html.
Finally, don’t go cheap on lawn seed. Buy either a single species mix with either perennial ryegrass or turf-type fescues or a mix of the two. Sometimes colonial bent grass and Kentucky bluegrass may be used but talk to a good seed person about including them in your plan. Avoid mixes with annual ryegrass as one of the ingredients. It only lives one year and slows the growth of the perennial grasses you want to establish.