When I was little, before the Thames Flood Barrier was finished, we lived in Twickenham, in a house by the river that would flood every single winter.
In the middle of the night you'd be woken by the strange amplified voices of policemen equipped with waders and loud-hailers, warning residents that the water was coming up; then in the morning there'd be a couple of sad, wet cars belonging to sound sleepers, parked in 2ft of water, that would never drive (or smell) the same way again.
Our front garden spent at least a week a year under water, and as a result, the planting had to change. Lavender and box edgings, with hopes of Mediterranean conditions, slowly edged themselves out of existence; roses, on the other hand, seemed to be able to stand it in the short-term.
But prolonged waterlogging is a serious problem for almost all plants, and there are several key signs to look for: leaves will go yellow or brown, and start to wilt; roots will start to die, and sometimes even bark will peel off. (Strangely, you see these most often in over-watered house plants – it's amazing the number of people who don't follow the simple "wait for soil to dry out before watering again" rule.)
If your garden is prone to getting waterlogged, you have a number of options. The first is to rethink drainage. Is water pooling after rain in particular places? Have you got a lot of not-terribly-well-laid concrete, flushing water at unhelpful angles?
Lawns with wet patches can be helped by a scarifying, even if it's just a once-over with a garden fork. If you are a person who likes the right tool for the job, I would probably not advise going for the Lawn Aerating Sandals (unless it's novelty present time) currently advertised on the internet, and I've also heard mixed things from users of hollow tine aerators, too (mostly moaning about how difficult it is to get the extracted soil plug out of the hollow tine). So I think the garden fork might still be the best option here. Walk over the lawn when it's next dry, making sets of holes every few inches. Add in a scattering of sharp sand over the surface, perhaps thicker where the water goes into puddles, to improve the texture of the very top layer of soil, where the grass is actually growing.
In flower beds, drainage can be problematic too. One key issue is to avoid walking on soil when it's wet, if at all possible. Compression when moist is the death of garden soils, most of the time. Adding lighter matter into the soil mix, such as cocoa shells and bark will help, as will gently mounding the soil of flower beds so that water has a little bit more angle to help run-off. And don't overwater in summer with chemical fertilisers, as you need to look after your worms, for their structure-creating properties.
If your garden looks as though it's going to be dampish for life, you need to change your shopping list with respect to stocking it. There are plenty of beautiful plants that suit sitting in wet conditions, and top of my picks would be the small, subtle tree Amelanchier lamarckii, which is just about to burst into spectacular white star-shaped blossom now (£47.99, crocus.co.uk). Underplant with camassia, the short-lived but heart-lifting blue star-shaped flower, imported from America's dampest prairies; or the native snakeshead fritillary, which fills the flood meadows of Oxfordshire with its strange, snaking patterns.
And for lovers of big leaves, there is paulownia (£12.50, burncoose.co.uk), the foxglove tree, which I've seen grown very successfully by friends with riverside gardens in easily floodable Kew. This tree will grow in the wild to 8m or more, but my Kew friends cunningly pollard it to the stump every couple of years, forcing it to produce delightful artificially gigantic leaves straight out of Jurassic Park. And not a loud-hailer in sight.