The soil is probably too wet and boggy to do much work on it at the moment but you can probably help get rid of the waterlogged areas but simply putting in a gardening fork as deep as it will go across the whole area and wriggling it around a little to create some drainage holes.. We do this with our lawn which occasionally develops boggy areas and it helps. Longer term you will need to break the clay up a little by adding in some sand or compost but if you add too too much you might run the risk of losing some of the moss and the moisture loving ferns.