// сохраняет сетку
procedure SaveGrid(Grid: TStringGrid; const FileName: string);
  var F: text;
      i,j: integer;
      RowCount, ColCount: integer;
  begin
    AssignFile(F, FileName);
    Rewrite(F);
    try
      RowCount:=Grid.RowCount;
      ColCount:=Grid.ColCount;
      WriteLn(F, RowCount, ColCount);
      for i:=0 to RowCount-1 do
        with Grid.Rows[i] do
        for j:=0 to ColCount-1 begin
            WriteLn(F, Strings[j]);
        end;
    finally
      CloseFile(F);
    end
  end;

// загружает сетку
procedure LoadGrid(Grid: TStringGrid; const FileName: string);
  var F: text;
      i,j: integer;
      RowCount, ColCount: integer;
      s: string;
  begin
    AssignFile(F, FileName);
    Reset(F);
    try
      ReadLn(F, RowCount, ColCount);
      Grid.RowCount:=RowCount;
      Grid.ColCount:=ColCount;
      for i:=0 to RowCount-1 do
        with Grid.Rows[i] do
        for j:=0 to ColCount-1 begin
            ReadLn(F, s);
            Strings[j]:=s;
        end;
    finally
      CloseFile(F);
    end;
  end;

...

// а так нужно использовать СэйвДиалог
if SaveDialog1.Execute then begin
      SaveGrid(StringGrid1, SaveDialog1.FileName);
end;