I have a Samsung Galaxy S phone from Verizon. I don't see the option to add the Google search widget like I have with other Android phones. Is there a simple way to add this without doing something as extensive as installing Cyanogen? I can't find the widget in the Market.
Long press on your home screen (any one from the home screens will do) a screen; called "Add to Home screen"; will popup, choose the option "Widgets". Another screen; "Choose widget"; will popup, start scrolling down till you find "Google Search", tap it and you will get the search options screen, pick what you want to go with, and it's all done. I'm running Froyo on a non rooted Samsung Galaxy S GT-I9000
Update: in case of that didn't work for you, you can get an application called z4root from the android market (the official market) and this will root your phone with one click (further more, it gives you the option of un-rooting your phone also by one click) then you will be free to do whatever you want without doing any extensive things. it works for both Eclair and Froyo, the only limitation is it doesn't work with NAND locked devices. http://forum.xda-developers.com/showthread.php?t=833953 and as you've said, you can use the enhanced search apk; here is a much descriptive link, still you will need a third party launcher