how do I place the twitter icon on my dock

On Mountain Lion, there's a function that automatically detects messages and Tweets. You're in the Mountain Lion support group right now, but your profile suggests you're using 10.7.x. I'm not conversant with pre-ML Twitter, but you should be able to drop the Twitter icon onto your Dock.

I'm pretty sure we can get the answer you need. Post in this thread!

Great - you're upgrading! One cool thing aout ML is that there's a Notifications function that automatically alerts you if you're getting a sweet. You'll have no problem at all.