If you have heavy clay soil, the only long term solution may be to dig a number of channels about a foot wide and 18" to 2 feet deep across your lawn and put down a thick layer of rubble, broken bricks etc. for soakaways. then rotivate the whole area, mixing in plenty of sand. This is a fairly drastic & time consuming solution and if you can't face this, the only short term solution would be to use a garden fork to make deep aeration holes every 12 inches over the whole of your lawn and brush a layer of sand over the lawn's surface so that a lot of it goes into the holes. if you adopt this latter course, I suggest you first give your lawn a thorough raking to remove any moss and mow it lightly as soon as it is dry enough to walk on. this will encourage the surface area to dry out more quickly and hopefully make the aeration holes work more effectively.