It sounds like you are trying to save the zip code as a raw number. Excel will remove the leading zeros because it doesn't need them to represent the number. If you want to save a zip code with zeros you have to wrap it in apostrophes like this '00790'
Agreed, although technically you only need to put one apostrophe (at the start). This is also useful when you want a formula to appear as text - eg '=1+2 would appear as =1+2 rather than 3.
If you don't want to edit an apostrophe into each cell, you can achieve the same thing by formatting the cells as text - right click on the highlighted cells, select Format Cells, then choose the 'Text' option from the category list.