Without the make and model of the unit which includes the clock this is all guess work, but it's guess work based on what you typed and lots of different clocks and radios.
You said "you push the Joystick right to enter the menu" then you said "Select adjust date/time" here is where the guessing starts.
you use UP/DOWN to change what is on the display, then RIGHT to select it.. right (or left to go up a level/exit)
Once you get into date time it displays the month.. UP/DOWN to select then right to go to DAY, again Up/down then RIGHT to go to YEAR, again up/down then RIGHT to HOUR Then Minute (Go to the next minute) then perhaps second
Then you are exiting to the left.
Exit to the right and it should start the clock
(or whatever action moves you to the next stage, that is what starts the clock, when you move to the "Next" stage after the last one)
Home is where I park it!