Sounds like you're wanting the equivalent of subforms within a form, like you would get in Access.
What I would do first is focus on how the information is stored.
Assuming you have your employees details stored in a list, which contains Name and ID, and have a separate list to store the shifts, with columns EmpID, Shift Worked, Date, Total Hours.
To display this, you can use DataViewWebParts in SharePoint Designer 2007 to link the two tables, and display the Shift data per Employee (this is done using a kind of "manual group-by", may require some XSLT hacking, though should be possible without touching any code).
Basically create a DataView of all the employees, and create a cell (either in a new column or in a row below the name) which displays a subtable to your shift data list.
The topics I mention here to read up on are "Linked Sources" and "Inserting Data As Subforms" in SharePoint Designer 2007, in case you want to read up elsewhere what I'm mentioning here.