There are several options.
A rough way (which however doesn't work if you are in Windows, or if you use a queuing system to launch ATK) is to issue the ATK command wrapped in shell "date" statements, that is
date ; atk myinputfile.py > logfile.log ; date
However, this will not print the date to the logfile (logfile.log), so we're much better off using Python (as usually is the case ;) ).
A quite fancy method, which also can calculate how long time the calculation took, is discussed in the manual (http://quantumwise.com/documents/manuals/ATK-2008.10/chap.tipstricks.html#sect1.tipstricks.timing).
The most convenient solution is, however, probably to just add these lines in the beginning and end of the input script:
import datetime
print "Calculation started:", datetime.datetime.now().replace(microsecond=0)
...
# ... original script ...
...
print "Calculation ended:", datetime.datetime.now().replace(microsecond=0)