As soon as the grass starts to dry out, mow your lawn once a week, beginning with the blades at the highest setting and gradually lowering them over the weeks.
Now that the grass is looking good, why not trim those edges to complete the look. You’ll be amazed at the difference it’ll make. Use long-handled shears or a grass trimmer.
Don’t be worried if you have bare or thin patches of grass, they can be thickened up by raking over the surface and then resowing seeds.
After all that, be surely to give your lawn a hearty meal. If it contains weeds or moss, treat these at the same time with a weed, feed and mosskiller treatment.