I have one of those after yesterday's rain. All we do is, when it has dried out, is spike it well and brush horticultural sand in.

Step one is to work out what is causing the waterlogging.
Most likely possibilities:
1. Wet winter and it will be fine in the summer
2. Compacted top surface through lots of use
3. High water table meaning it is difficult for water to drain away
4. Hard pan - caused by minerals forming an impervious layer a foot or so down (stopping water draining away)
Solutions:
1 or 2 - aerate the lawn with a garden fork or machine to improve drainage and air flow to help the grass grow, then top dress it with fine sand to fill the holes you made while aerating the lawn.
3 or 4 - Will probably need drainage of some sort being installed or, consider changing the use for that area to being a pond, or bog garden.
Suggestion: Try aerating the lawn and top dressing with sand, if that doesn't work then you may have to consider the more drastic option.

I should think everyone's is waterlogged after the rain we've all had!