Good techniques for stirring dough

You generally don't stir cake batter at all.

Where I learned to bake, we were taught that if you want a light and fluffy cake, as is generally the case, then you should fold in the dry ingredients (including flour). That means using a flat surface - a silicone spatula works great but you could even use your hand in a pinch - sliding it down the edge of the bowl, and using a turning motion (i.e. folding) to incorporate the flour, repeating several times until there are no longer any large clumps of dry ingredients.

When you fold, it's very difficult to over-mix. And particularly with cakes and quick breads, under-mixing a little is actually OK, because the batter tends to be quite moist and eventually the moisture will seep through to any unincorporated flour - and if it doesn't, you'll get a nice spongy texture.

Commercial mixers actually have paddle attachments for folding large amounts of batter. You don't need a special mixer, though; you just need to be gentle and conservative with your mixing.

Not every cake is the same, and some recipes may specifically call for you to whisk the batter (for which you should use a balloon whisk, not a spoon or spatula) instead of folding, but if it just says to "mix" the batter then I would using the folding technique.

Well, I can answer now that I know it's a cake --

Most cakes don't need to be fully mixed. So long as you don't have large lumps of flour (which you won't if you sift it, but you can also take a wisk to the dry goods if you're lazy like I am), it'll be fine after it's baked.

If you overmix most types of cakes, you'll get 'tunneling' where the gluten traps larger air bubbles, which end up looking like a worm's been tunneling through the cake. (it seems to happen the most w/ the muffin method).

Personally, I use a mixer for cakes (hand mixer normally, but I'll break out the stand mixer if I'm making really large cakes) If you don't have one, stick with a wooden spoon or a spatula. You can even fold in the flour, if you think you might've been mixing it too much.

Here are a couple suggestions:

Sift the flour

Use a low gluten flour (cake flour)

separate the yolks and whites, beat whites and fold into your batter (dough) as last step in the mixing process (makes it lighter)

Use a spatula instead of a whisk to do the mixing, or the paddle attachment on your mixer.

Cake batter is usually mixed using the creaming method. Start with room-temperature butter and the sugar. Beat until light and fluffy. Then you can add your eggs slowly, and add your dry ingredients once all the wet ones are mixed.

Like Aaronut said, not all cakes are created equal. Different cakes may call for a different method, but the creaming method is usually best for light, fluffy cakes.