I can't find the Timex T229B on the Timex support site. However, the T228B may be similar. To turn off the alarm completely, there is a switch on the left side that must be set to Off. The switch is labeled Alarm on one side and Radio on the other. In between are 4 positions - from front to back, Radio, Buzz, Off and On. When in the Off position the alarm indicator symbol will not be lit at the top left of the display (it looks a bit like a bell). The dimmer switch is in front of this Alarm/Radio switch on this side of the clock.
To turn off the alarm and reset it for the next day, press the Alarm Set/Reset button to the right of the hour and minute buttons. The Snooze button is the large button to the left of the hour and minute buttons.
Timex alarm clock and clock radio manuals are available here: http://www.timexaudio.com/product_manuals.asp
I hope this helps.