Waterlogged garden help???

Hi after having alot of rain lately my garden has become waterlogged. My soil is also heavy clay so it doesnt help. Im just wondering what i can do as im doing a project on the garden at the moment. I dug a hole and it filled within 2 seconds of digging. Ive heard about french drains how do i do those. I cant afford proper installation of drainage pipes. If i can make it abit better and then plant plants that dont mind standing in abit of water? which plants would you recommened for that?
I show some pictures i did yesterday of the water any advice would be great

 

Plant on top of the ground and mound up soil around the root system .. this will give your plants better drainage
OR plant in raised beds
As for the flooding ... unless you have somewhere lower for drains to run to your best bet is simply to wait until nature takes its course

 

I'd go with what Whis4ey said. Flat gardens are boring anyway. How much space do you have? Perhaps you could bank the soil up, and put a little pond in the lowest bit. Maybe you could get a tonne of sharp sand from the builder's merchants (about £35 delivered) to mix in with the clay soil when banking it up so as to further improve drainage.

The french drain thing, if I understand correctly, is what my dad's farmer pals call a field drain. You dig a trench, fill it with rubble and gravel, then bury it again. They clog up after a few years. You can also get proper pipes with holes in to do the same job, but I've heard that they too clog after a few years. In any case, the water has to go somewhere, so if you don't have somewhere lower for it to drain to it won't solve your problem. It also means you can't dig where the drain runs.

There's a field drain on my land. It is impossible to forget where it is, you just follow the perfectly straight line of marsh grass that wouldn't grow there if the drain was working

 

Another thing that might be relevent if you have a modern house. When they build them they drive heavy machinery all round the future gardens. In wet weather particularly it squashes the clay down to form a very compact layer that water cannot soak through. Sometimes double digging can help break through that hard pan and help.
If you are in such a situation it is a good way of getting fit and you will end up with a skip or two of rubbish cause builders just chuck the rubbish down and put a layer of soil?? over and expect people to be able to have a garden.
However it does help with clay to have a lower area to drain to. On some land I am renting I am digging out an open ditch. It is clay and I can already see the water table dropping in my polytunnel. I have had to suspend ditch digging cause it is filling up - I hope we get some prolonged dry weather.

 

All this rain is dreadful. Now they're telling us it's the wettest November we've ever had since records began. Great! I hope the above answers have helped, Natty.