Does anyone know how to add two W-2s from the same employer, different time periods. It seems to delete the first one. I entered each one in myself.

Different time periods in the same tax year from the same employer should be reported on the same Form W-2.  Are you trying to enter forms from more than one year? 

What boxes are filled in on them?  Could one just be a continuation?

If the EIN number is the same and you work in more than 1 state or city, sometimes they will give you another W2 with the extra state information on it and the top part the same or not filled in.  If this is the case, list one W-2 but include both state or local  taxes on it.  It will let you type in more than one line for boxes 15-20.  Don't add the boxes together.  

Same for boxes 12 & 14 if there is no room on the first W2 they can give you another W2 with the extra boxes on it.  So list them all on 1 W2.  For box 12 just enter it in the next row or box.  It doesn't have to match the box 12a-d etc.