Hi, the way to improve soil including drainage, is to add and work in lots of compost.
ciao

...And if it still stays wet even with the addition of compost or other organic material, that's great. Wet shade is a wonderful environment in which to garden:

Ferns
Hostas
Ligularia
Impatiens
Foam Flower
Coral Bells
Moss

and the list goes on

You might want to add some sand too. Our shade garden beds (clay area here too, plus I add compost and top with shredded hardwood mulch) were too damp and fungal until I got smart and worked in sharp (builders) sand each time I amended the soil. It depends on how much air circulation your beds get, of course, but here some sand was needed to improve drainage. If you want to get really fancy and spend big bucks, you could add greensand, but just a tad.

If your soil is clay, adding sand will give you two thirds of the recipe for bricks (straw being the third, watch the movie Moses sometime if you get a chance, notice what he is stomping in). I don't think plants will grow well in brick. Add soil conditioner (partially composted ground pinebark) and compost. In my master gardener class it was taught that the soil should contain 30% of decaying wood material which provides air circulation, moisture retention and minute organism.

Ok, the movie isn't Moses it's The Ten Commandments but the point is correct about the ingredients for bricks. If your soil is sticky then it's clay. Sorry. I'm four years into a front yard very similar and having done it the wrong way two of those years, I'll tell you that you'll save yourself digging up plants or garden beds later if you properly prepare the soil now. Go get some of the really crappy bark mulch, you know, the stuff that's not consistently shredded, some of it's teeny some is huge chunks of wood, and mix that in as best you can. Do your best to dig down to a fairly decent depth, depending on what you may eventually want to plant there. Sadly, I had decided I "needed" rhododendrons and azaleas so I ended up pulling out and re-digging significantly deeper after they'd been in the ground a year. I also dump in some of Wal-Mart's extra cheap "potting" soil (blue bags) which is actually their composted manure mixed with tiny white gravel. My plants have been extremely happy with an equal parts mix of the bark mulch, "potting" soil and the gooey native clay we have here. Remember to top the bed off with a nice healthy layer of mulch - this makes even the shoddiest gardening effort look ten times better to the untrained eye, which is a factor in all but completely walled in gardens. Remember if you feed your soil like this your plants will take care of themselves by being much stronger, putting out healthier root systems and lasting longer than if you amend hole-by-hole or try to "layer" instead of digging in your amendments. If your clay is anything like mine, pick up a bottle of Ibuprofen along with the mulch and (compost) potting soil!