My back garden is very boggy ground and it is located in the midlands in Ireland, so this is common. I tried planting trees to take the excess water and that seemed to help for nearly a year, but in Ireland we get lots of rain.
Are there any easy solutions to my problem without having to do a lot of work?
There are different reasons why your ground could be so wet, I don't know the situation in Ireland, but here in the Netherlands we can have boggy ground as well.
Different reasons are:
It depends on the cause to find the right solution.
If it is clay ground you have that is causing the problem, one easy way to deal with it is to add organic matter to your soil. This will soak up water.
If your soil is not tended for a while, you can dig or plough the soil.
For the third reason, you'll need to make vertical drainage holes that reach the ground water level, and fill these holes with something that will drain well (shells, lava rocks, etc.).
The last reason (ground water level), is not something to easily change, unless you want to build dykes, just as we do in the Netherlands...
So the easiest solution in my opinion is to add organic matter to the soil, in order to soak up much of the water in the soil. For organic matter, think of compost or peat.
Adding Organic matter is not a permanent solution, I would advice adding some fine material like sand might help air out the ground it worked for me....Also try adding more shrubs to try draw up the extra moisture
There are a few things you could do that would work; one would be a 'dry well' that collects the water to slowly be dispersed into the ground without creating mud out of the surface. This is pretty easy; dig a big trench in the middle of that lawn 10'X 2', install landscape fabric, fill with rounded cobble or 1 1/2" drain rock. Cover with landscape fabric and then more cobble. The water has a place to go, collect and still be allowed to filter through to the ground water system.
A little more expensive but not much would be turning this area into a graveled surface, 4" deep, using landscape fabric below the gravel. Rent a sod cutter, take out all of the sod (use that soil, mud and grass for creating plant beds), dig down another 2" use that soil on top of the piles of sod you've made into plant beds, use pt 2X4's secured with stakes where you need a clean edge, lay the landscape fabric down, install the gravel (5/8 or 3/8 minus crushed gravel no larger), use a compactor that you can rent and you'll have a nice new clean and usable outdoor room. 
