Setting the alarm on my clock radio

Can you comment with the model number? It will be on the information sticker on the radio itself. It will possibly start with 'CRX-'.
Try this - Press and hold the alarm set button until the display flashes like your setting the alarm time. Click the same button again and it should swap between buzzer and radio each time you click it. It will probably show some sort of logo on the display telling you which it is set to.

Denis, use the time set buttons, normally labeled either hours or minutes.
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I love the form of your question, as I wanted to wing the sucker myself, but got online before I actually pulled an Office Space on it. I found nothing, but I DID actually figure it out. Not super intuitive though. To set the time: Hold down the memory key in the middle until the number flashes. Use the arrow up/down on the right to set hour. Press Memory key again, repeat with arrow keys to set minutes. Hit memory key again. Alarm: Press/hold the Alarm button until the Alarm 1 or 2 flashes and press the side you want, 1 or 2, to set. Arrow time up/down, then do minutes, press alarm 1 again, select alarm or tuner, press alarm 1 again. Now I need to see if it will work in the morning. I know the flipping time is set though! Good luck. If you wing it, please post photos! :D

There are 2 common mistakes with radio alarm clocks. 1) You have AM/PM backwards either on the actual time or alarm time 2) The volume is mistakenly set all the way down

There are three buttons under the heading "Dual Wake", WK1, Cancel, WK2. The WK buttons refer to the two wake time settings you can have. Press Cancel and then WKx. That will turn off the alarm. If you press WKx more than once, it will cycle through small symbols on the bottom of the screen with the number x in front of them. First symbol means it will have a sound alarm for alarm x, second symbol means it will have a radio alarm and the third symbol means it will play the CD to alarm. You set the time for alarm with the slide switch at the back of the unit, selecting WK1 for alarm 1 and WK2 for alarm 2. You can have both alarms active at once, or either one singly.

I just did the trial and error thing. it's okay now. thanks

HOW does one set the time and alarm on a "sony dream machine clock radio"?

hit the cancel button then the wake1 or wake2 button as you need to cancel them.

To turn alarm off completely, press WAKE1 and WAKE2 until the bell-shaped indicators go off.  
As for resetting the alarm (buzzer), press SET WAKE/CLOCK untill SET and WAKE! light.  Press left- or right+ arrow to set time.  Press WAKE1 until bell-shaped indicator comes on.