Usually in Linux you use crontab for this kind of scduled tasks. But you have to specify the time when you "setup the timer" - so if you want it to be configurable in the file itself, you will have to create some mechanism to do that.
But in general, you would use for example:
30 1 * * 5 /path/to/script/script.sh
Would execute the script every Friday at 1:30 (AM)
Here:
30 is minutes
1 is hour
next 2 *'s are day of month and month (in that order) and 5 is weekday
This code line executes "ls -l" at a specific time. This is an example of executing something (a command in my example) at a specific time. "at" is the command you were really looking for. You can read the specifications here:
Cron is good for something that will run periodically, like every Saturday at 4am. There's also anacron, which works around power shutdowns, sleeps, and whatnot. As well as at.
But for a one-off solution, that doesn't require root or anything, you can just use date to compute the seconds-since-epoch of the target time as well as the present time, then use expr to find the difference, and sleep that many seconds.