Tap and hold your Palm's stylus on the handwriting recognizer button until a little menu pops up, then select "Bottom" from that menu to put the recognizer on the bottom of the screen. In the handwriting recognizer control buttons, you should see one with a downward-pointing arrow between three lines; tap on that button to collapse the handwriting recognizer controls to a little bar at the bottom of the screen. If you see a red "OFF" button, tap on it to turn it into a green "ON". Once you've done that, you can write characters anywhere on the screen and tap on the 'zi' character button to recognize them.
If this doesn't sound like the way handwriting recognition worked on your old Palm, it may be that you had another handwriting recognizer program installed somewhere - do you remember seeing a "PenPower" or "PalmDragon" icon in your old Palm's application launcher screen?
