You can start with the dead leaves laying around. Rake them up, and bag them in lawn bags to rid of them. Then the lawn, bringing it back from cold winter months, it needs to start breathing again. So why not do a aeration, and break up the soil that is now compacted. Aeration will create tiny air pockets that you can then fill with your compost.
When you are done aeration on the lawn, you can then spread a thin layer of peat moss over your lawn with a rake. This is called a top dressing. It helps to toughen your lawn and make it resist to thatch, disease and growing of weeds.
Speaking of weeds, maybe they need to be whacked. Also give your lawn some nutrients and care it will need, by keeping weeds out. You can also apply a weed killer for those pesty weeds. Also putting crabgrass controler is a good idea.
Don't forget to prevent those small creatures that can invade your lawn. Those little critters are easy to control with a good pesticide. When planting try to use disease resistant plants. They help keep fungi, and bacteria from doing damage to your lawn as well as your garden.
Oh then there are the bare spots that can happen for many reason's. The dog's are one good reason. You can fill the bare spot with a patch, like top grade topsoil. After scatter grass seed over the spot. In that spot try not to plant to much seed. Rake the spot lightly and spread a thing layer of your compost over it. Your seeds should be watered on a daily basis, but never to soggy.
Since grooming your backyard is really not that hard, why not mow the grass, and trim some tree's and shrubs if you have them. Just by clipping the hedges, pruning some plants and edging can give you a really big head summer start.
Powerwashing the patio furniture and deck isn't a bad idea either.
Old man winter can also do havoc on your fence. If it's wood, check for cracks, loose boards. If metal, check for rust and any loose or missing clamps.
And when your all done, why not throw some steaks on the grill, and admire your hard work.