The immediate cause of that error is that the Worksheet object type is specific to Excel and doesn't exist in Word. There's a lot more to this, though, because Word doesn't work much like Excel in other respects.
The big one is that while rows, columns, and cells always exist in Excel, they don't exist in a Word document unless the document contains a table. The userform could put data into cells of an existing table, or it could insert a new table (during which the code would have to know how many columns to create). Most likely, the code should add a new row to the table for each press of the Save Entry button, because you won't know in advance how many rows there will be.
Here's a version of the Save_Entry_Click procedure that runs in Word. It assumes that there is already a table in the current document, presumably inherited from the template on which the document is based. It further assumes that table is the first (or only) one in the document, and that it has at least 8 columns (probably with the column headings already in place).
Private Sub Save_Entry_Click()
'Copy input values to table in document.
Dim lRow As Long
Dim tbl As Table
Set tbl = ActiveDocument.Tables(1)
tbl.Rows.Add ' defaults to adding one row to bottom of table
lRow = tbl.Rows.Count
With tbl.Rows(lRow)
.Cells(1).Range.Text = Me.NoOfPeople.Value
.Cells(2).Range.Text = Me.First_Name.Value
.Cells(3).Range.Text = Me.Last_Name.Value
.Cells(4).Range.Text = Me.Final_Format.Value
.Cells(5).Range.Text = Me.Address.Value
.Cells(6).Range.Text = Me.City.Value
.Cells(7).Range.Text = Me.State.Value
.Cells(8).Range.Text = Me.Zipcode.Value
End With
'Clear input controls.
Me.NoOfPeople.Value = ""
Me.First_Name.Value = ""
Me.Last_Name.Value = ""
Me.Final_Format.Value = ""
Me.Address.Value = ""
Me.City.Value = ""
Me.State.Clear
Me.State.Value = ""
Me.Zipcode.Value = ""
End Sub
Note the addition of the statement Me.State.Clear near the end. It removes all the entries from the dropdown list. This should be in the Excel version, too; otherwise, each time the user clicks the down arrow of the State dropdown, the code will add a complete new set of abbreviations to the existing list.
While this code does what it says on the label, it isn't complete for practical use. It needs error handling. As a simple example, if the user clicks the Save Entry button when all the fields are blank, the code will happily add a blank row to the table. If for any reason the document doesn't contain any tables, or if the first table in the document doesn't contain at least 8 columns, the code will throw an error (and the default error message won't mean anything to the user). There's nothing to check that the text in the State field is one of the abbreviations in the list, or that the Zipcode entry is a valid set of digits.