Welcome To TBN!!
As mentioned previously, getting the area you want to turn into an arena dry is first and foremost. Some questions immediately come to mind.
1. Why is the area wet to begin with?
2. Is is because of the natural grade causing the water to naturally flow toward that area?
3. Is there a natural spring in that area?
If it is because of grade, simply add some kind of fill.
If there is a natural spring in the proposed area, I would suggest relocating it.
Depending on where you live and how fast you want you want to get this completed will often have a big impact on the cost. Often times being at the right place at the right time, you may get lucky with someone wanting to find a home for fill, and if your lucky, lots of it!
Keeping the base slightly above the local grade will keep water flowing away and obviously keep the area dryer, but not too high as erosion issues develope. Tile may of may not be needed. The area should also have a very slight crown to facilitate drainage and hopefully prevent water from puddling up.
Have you tried local farmers for doing the grade work, with you buying the materials?
Also, have you discussed this with other arena owners to hear their good and bad points?
Your location will have a big impact on matieials based on what is available.
I know other TBN members would love some pictures of the proposed location. :thumbsup: