Firstly, forgive my ignorance on lawn care. Here's my problem:

My lawn takes a lot of drainage from another elevated site behind my own hence the soil is compacted and very damp. The end result is that moss has taken over. I know I can't kill it once and for all. So far I've used an electric moss raker which certainly seems to have cleared the majority and I've aerated the lawn.

Now...what should I do next to give me a healthy lawn come the summer?

Should I apply an organic compost/sharpsand mix over the lawn then resow or am I being very naive. Your advice would be most welcome!!