Your best bet is to look out for a time registration system based on a database back-end. There are plenty of those around I'm sure.
If you insist on Excel:
It is possible to do this in one workbook, but requires macro's and isn't very secure. A knowledgable person would be able to view other people's data quite easily. It would be a lot safer to have a separate workbook for each person. Password protect those files with a file, open password you only hand over to each person in question and you ensure people wont easily get in other peoples data. Even better: let IT set up a separate folder on a network drive for each individual exclusively (and accessible to you) and put their files in there.
After that you can use Data, Get Data, From File, From folder to fecth the data from all those workbooks if you make sure the layout of these separate workbooks stays exactly the same.