There is another easy way to do it. I tried it in mine and it worked. So I see no reason why it shouldn't work in yours. I had earlier gone to the Fonts De-uglification link too, but it seemed a bit complicated for a new user like me.
So, as suggested by others, I copied (as root) all the windows fonts I need (including Tahoma) to my fonts directory which in my case, is located at /usr/X11R6/lib/X11/fonts/TTF
Then I ran the command:
to update the fonts.dir and fonts.scale
It worked - now I can use all the fonts I copied over, in OpenOffice.
Hope it helps.