If it's clay soil that's easy to dig in the wet months, here's what you can do. At the community garden, one of the gardeners is able to dig in unused plots any time of year by running a very slow trickle of water -- slow enough so the water soaks into the soil instead of running off. If it runs off, it's too fast. Once the soil is moistened enough, she can dig easily. If she's working on a larger area, she keeps moving the trickle of water over. Without that small amount of water, the soil can be like concrete in the summer.

If the soil is workable, I like to use a digging fork. They seem to be hard to find in nurseries and hardware stores, but the best kind for hard soil has tines with a square cross-section, not flat (rectangular cross-section). The only caution is not to use them as a pry bar. I broke the handle off a really nice digging fork once by trying to pry up some blackberry roots.

Hmm, I'm also wondering what roots you're digging through. If they're oaks, be careful not to disturb them too close to the trunk.

I have a 3' tire iron in the same place in my garage forever that just plows through clay tough soil to planr and for tough weeds and this is how I get the biggest rocks from deep in my gardens which I had alot when I was planting my rose beds or digging up old grass. Even the sharpest shovel won't get into that but I do have a pitch for that has helped me on many occasions especially with deep rocks which you have way down that eventually stunts the growth of everything. After digging the holes or just loosening the soil I ammend that soil with SuperSoil Ammendment and since my clay soil is such a hatd mess also mixed this with Supersoil Cactus some used coffee grounds and whatever else you have laying around but the Supersoil really has everything and this will keep the ground so nice for a couple of years till it begs for that again but it's usually fine and even weeds aren't as difficult to pull as in the past. Amazing amount of worms just love this mixture so you'll get great blooms. So grab the tire iron from your car or get on for your very best tool ever because it won't bend and is always sharp and heavy to get into those nasty grounds.

I use a Bosch Brute 66 pound electric jack hammer and a clay spade to dig holes in my rock hard clay soil. Before I had the jackhammer I used a mattock to dig a small hole, filled it with water, waited overnight to let it soak in and soften the soil, and then used a regular long handled shovel to finish the hole.
If you are rototilling hard clay, here in California you have to wait for the rare two or three inch rain we sometimes get in the winter to wet the top six inches of the soil. Wait a few days for it to partially dry out and then rototill it. If the soil is too dry the rototiller blades will just bounce off it, if too wet the clay will stick to everything and compact right down again. Timing is everything.

Pretty much what everyone else said. Letting the soil soak makes it much easier to work. I also use a digging fork. I didn't have one until not too long ago, but it sure is much much easier to use than a regular garden spade. I don't hit nearly as many rocks/concrete chunks anymore, meaning I can dig deeper, and I cam simply stick it in and wiggle it around to loosen all of the dirt. It's also great for digging up fall bulbs, since you hardly tend to stab or cut them in half.

As Debby said, I also add as much organic matter as I can get my hands on. Worms especially seem to love the used coffee grounds that I pick up at Starbucks. Compost is even better, since too much coffee grounds tend to produce slime molds occasionally in the garden. (I thought something threw up on my plants at first, but after a little research it turns out it's slime mold from the grounds - when I didn't have compost to add at the time). You might be able to find some compost for free at your local recycling place.

Digging forks and mattocks, definitely. Using a shovel on hard clay will wear you out way too fast. I've also used gypsum and liquid soil penetrants, which seem to help soften up the ground. Of course, you have to water them in, so it's possible the water is doing all or most of the work.

As above, but also a post hole digger: you know, the ones with two paralell shovel like blades and two handles.