there is NO search field on my iTunes?!

Make sure you have the latest updates for OSX and iTunes by clicking the Apple in the upper left corner of the screen, then clicking Software Update.

You should see a search box in the upper right corner of the screen.

More info how to Search here -> iTunes 10 for Mac: Search your library or a playlist

Are you also missing the red, yellow and green buttons at top left? This sometimes happens due to a bug which ocasionally surfaces.

If this is the case, click and hold on the very bottom right corner of the window and drag it diagonally upwards to reduce the height of the window.

Then click and hold on the bottom bar of the window and drag it downwards to reveal the coloured button, controls and search field in the toolbar.