Some back-of-the-napkin thoughts (so, if I'm getting things wrong or forgetting things, please correct and/or add in, folks!):
In my
experience and from what I've read, if you're not in a desert situation, techniques like
hugelkultur that are raised rather than sunken may work better for you, because you're likely to see a lot more precipitation in a year than the 13 inches that we see here in southeast Arizona, for example. How many inches of annual precipitation do you get there, and how are they distributed through time?
For us, dams and seguias (channels to direct water) from Middle Eastern foggara systems (more great traditional techniques from the Sahel!) combine well with sunken beds full of organic matter -- like modifications of Zuni waffle beds as well as smaller indentations like zai, in different applications -- because we rarely get rain. In certain seasons, though, we get daily rain and some torrential rain, which we need to be able to control and then hold against the long dry times.
For you, you may well need more and better drainage lest you end up with things too soggy. That's where raised beds, especially when full of organic matter, come in.
In various parts of Africa (even some arid parts, if I understand right), this is accomplished by mounding with a hoe in combination with adding organic matter, then planting into the mounds. This may be simpler and more easily accomplished for you than building
hugelkultur beds, for example.
From the Penniman book I cited before, there's a good section on "bed forming" that describes a process of smothering existing vegetation (like with tarps temporarily applied, or
cardboard or other biodegradable material you intend to remain there and break down over time) and then moving soil from your pathways to your beds. If the ground is currently thick with vegetation like sod, cutting and flipping it, then seeding a cover crop, then coming back and turning all that organic matter into your new raised beds could accomplish much of the addition of organic matter (pp. 130-131). The Ovambo of Northern Namibia add "manure, ashes, termite earth,
cattle urine, muck from wetlands, and other organic matter to increase the fertility of their mounds" (Penniman, pp. 74-75).
Your pathways should also help drain and move away floodwater when necessary, functioning like the systems of dikes and canals built to move water away from waterlogged soils e.g. by farmers in the Rio Nunez region of Guinea (p. 141). You could mulch them or plant a cover crop like clover there.
One shared thing here is adding organic matter. The more organic matter you can add to help retain moisture, the less you should have to pump and add groundwater to the system in between rains.
Keeping the ground covered with plants and/or mulch is also important in both situations, to prevent topsoil loss and excessive evaporation as well as to help any floodwater sink in rather than rushing across the
land, carrying everything away with it.
Also, what kind of slope are you on? That will help to determine what solutions will work best for you as well.
Sorry for the current obsession with Penniman's book, but it is just
so good and inspiring. Highly recommended.