Select the cells you want to print (shift-arrow or click-drag). Open the Format menu and use Borders and Shading. The Borders tab has numerous options for visible borders.
In Microsoft Word, the table should be inserted by the table option in the tool bar. If its is drawn by auto shapes option you will encounter these problems.
This answer will vary slightly by version of Microsoft Word, but for Word 2003, click Table, Table Properties, then in the Table Properties window, click Borders and Shading, then select your option, including All or Box. Click OK twice. The borders / lines should now print just fine. If not, use thicker lines to troubleshoot further.
Select the cells you want to have the lines around and right click. Select format cells and then border. chose which border style and select all of the lines in the box so that it has borders on the inside and outside
You can't print the grid lines in Microsoft Word. Though, never fear. There is a way that you can make them print. You just need to add a border around your table and I believe also in the cells and you will have the lines that you want. I hope this helped.
Mouse over the table. A "+" will appear in the upper left corner. Right-click on it and choose "Borders And Shading" from the flyout menu. On the Borders tab, click "All", set Color to black (or whatever you like) and click OK. Now the lines will print.