This is a DataGrid and not a DataGridView, right? DataGrids are weird in that you have to make a table style to the grid and add columns to the table style to get what you want. DataGrids aren't a storage medium, they're a presentation tool so you can't store rows in the grid itself. What you probably want is a DataView on your table that you can use as the data source for the grid. That gives you more control over what's presented.
If possible I recommend that you move to a DataGridView for .NET 2.0. It's a lot easier to figure out and you can do more with it with less work.

If it's not possible to switch,
this is a good FAQ for Windows Forms in .NET 1.1 and
this is an article that addresses how to use table styles and columns. It should get you started.
If you have any questions about the specifics, I'll be happy to help.
The truth does not change according to our ability to stomach it.