To upgrade, click on the particular turret you want to upgrade. You'll see the word "Upgrade" in green in the lower right area of the screen, assuming you have the money to do that upgrade.
My upgrade strategy is to power-up the units that have traffic on both sides first, followed by the units that I place across the entrances. I try to get a majority of my towers to the same level, but I concentrate on plasma turrets first, then SAMs, then freeze guns. I place sonic turrets at the end of rows, where the enemies go around 3 sides, thus maximizing the damage. DCAs go in the center areas.
"I have a hammer! I can put things together! I can knock things apart! I can alter my environment at will and make an incredible din all the while! Ah, it'* great to be male!"