Welcome to the forum, sgardne!
It might be possible to install a drain field, although I had 5 different landscapers look at my yard with that in mind, and they all told me it wouldn't work. I'm still not sure I understand why. I even had a soil engineer come out to look at the yard, because I was thinking of having soil brought in to fill it. He told me the water table was very high here, and adding soil on top would not work. I'm not sure I understand the "why" of that, either. But, I've lived with it for over 30 years, now, and managed fine.
Your best option, IMO, would be to create raised beds. If you prefer not to do that, then it would be important to consider what time of the year your property floods and what plants you want to grow. For instance, I have no trouble with standing water during the summer months, so I can grow just about anything in my yard. Problems arise when I want to plant trees, shrubs, or perennials, because they'll have to survive the wet times. I have lost several plants to standing water.
After all these years, I'm pretty familiar with the exact "wet spots" in my yard, and if I want to plant, say, a new rhododendron, I know where not
to place it.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams