TIM = Thermal Interface Material. Just a catch-all name for thermal paste I use to keep from typing 'thermal paste' all the time.
No, you don't let the alcohol drop dry. You use it to dissolve the old paste and wipe it away.
I usually first wipe as much away as I can with the coffee filter dry. Then, Just put enough ArctiClean 1 (or isopropyl alcohol) on the CPU to cover the left-over paste on it. Let it sit for about 30 sec and then wipe it off with a clean coffee filter. Do the same for the cooler base. Try not to get any cleaner on anything else! Don't let it run off the CPU onto the socket or board. Give the clean surfaces a minute or so to dry before continuing.
If you use the above ArctiClean Kit, you can repeat the process with the ArctiClean 2 Thermal Surface Purifier to leave the surface in like-new condition. Then just use the pea-size dab of thermal paste on the center of the CPU. Let the pressure and heat of the cooler spread it by itself. No need to spread it around. And remember, better to use too little paste than too much. All you're trying to accomplish is to leave a thin film between surfaces to fill in the microscopic pores of the metal. I use this for thermal paste:
http://www.amazon.com/ARCTIC-MX-4-Carbon-Based-Thermal-Compound/dp/B0045JCFLY/ref=sr_1_1?s=electronics&ie=UTF8&qid=1400008939&sr=1-1&keywords=mx-4
I like it because it's not electrically conductive if it some touches the socket or board (where it shouldn't be).
Once you set the cooler on the paste, try not to raise it back up again. That's when the air bubbles form. If you have to, then start over with the application as noted above.