There is considerable documentation on the Joomla.org website regarding this (check the forums and help sections), but you should understand:
1) Joomla! 1.5 is not stable ... they have just recently released RC4 - you may want to consider waiting until 1.5 stable is released (and maybe a little bit after that, so that any last minute bugs can be identified and squished).
2) The path from Joomla! 1.0.x to 1.t is not really an upgrade as much as it is a "migration". The process is considerably different than a traditional Joomla! upgrade, and involves some migration scripts.
3) If you do this before DH upgrades their "one-click" installer, you will loose the ability to have the "one-click" upgrades. This is fine for me, but others prefer to retain that convenience.
4) Be aware that many of the commonly used extensions for Joomla! are not yet compatible with Joomla! 1.5, and most probably will not be (compatible) until 1.5 goes "stable" (and it may even take a while after that).