We have some old IKEA kitchen units that we want to paint in eggshell.
I wanted advice on the best preparation for the doors.
My only experience with painting wood has been re-glossing doors etc. and I haven't used eggshell paint before.
Use one coat of a clear or white latex primer. I'm assuming you meant an opaque paint with an eggshell finish, not a stain.
Assuming the kitchen unit doors are solid wood (not covered/laminated some how):
All of the above & more can be seen here: How to Paint Kitchen Cabinets via This Old House