I always make cookies by hand. Always have, always will. And my cookies are delicious. As betteirene suggests, make sure your butter is room temperature. Get into a little rhythm with your stirring (all in the same direction, please) and use a sturdy spoon with a large shallow bowl (bowl of the spoon that is) that feels well balanced when you use it. It probably takes a bit more patience but you are rewarded with not having to clean any beaters. Have fun! ;o)

Everybody else is absolutely right; the hardest part is having the arm oomph to stir in the flour. There was a time when we didn't have a stand mixer and I made a deal with my husband: if he did the tedious mixing-in of the flour, I'd do the baking. Somehow, we did not renegotiate when we finally got a Kitchenaid. Now he just flips a switch and I stand there baking all afternoon. Hmm.

Ah, to have access to small-grained sugar...even the smaller-gained castor sugar I can buy here is so much more of a pain to cream than the sugar you get in the US...
Doing it by hand is a real schlep. Even an in-expensive hand mixer will make it so much easier...

There are times when digging the mixer out of its cabinet is a real drag, as it was a few nights ago when I wanted to make a batch of Toll House Cookies but the grandkids weren't quite asleep. They hear the mixer and they come runnin', the same way the cats do when they hear the sound of a can being opened, and I can't get them out from underfoot--the cats or the kids.

"Creaming" means to combine ingredients, usually butter and sugar (and sometimes the addition of eggs) until the mixture has increased its volume, is light and fluffy, like whipped cream, and the grains of sugar can no longer be seen or felt in the mixture. This puts a lot of air bubbles into the mixture, and the leavener (baking soda) causes those air bubbles to expand, which gives cookies their rise. If you don't cream, the result is those thin, flat, wide cookies with chocolate chips poking through.

Do what I do when I can't or don't want to use a mixer: Pretend you're Laura Ingalls Wilder! Be a real pioneer woman! It's very easy to blend the sugars and butter together with a wooden spoon when the butter is at room temperature or slightly warmer, but it takes about 10 minutes of active stirring.

And if you're anticipating that your arm will get tired, you can cheat: Stir together the softened butter and the two sugars, then blend in very well the eggs and vanilla; stir in the flour, baking soda and salt, then add two additional tablespoons of flour. Dump in the chocolate chips and combine. Drop tablespoon-sized balls onto cookie sheets and refrigerate for 15-20 minutes before baking. The combination of a little more flour with chilling the dough will give your cookies some shape without greatly affecting the taste.

Yes, you can do it by hand. But, I think the hard part is going to be combining the flour with the rest of your ingredients. I would start by combining the sugar and the butter (at room temp) and then build the dough like a pasta dough and finish by adding the chocolate chip using a kneading methed or if dough is soft enough then fold in normally. Good luck!

The hardest part is going to be creaming the butter and sugar by hand. There is a Cooks Illustrated recipe for chocolate chip cookies that melts the butter, and mixes everything by hand. Melting the butter increases the chewiness.