Getting Started

You will need:

a copy of the US version of Dragon Warrior Randomzier.

An NES emulator. I personally use BizHawk.

You can find these using your favorite search engine.

Go to dwrandomizer.com load in the ROM where it asks for the Rom File, and click Randomize! You'll be given an NES rom, this is your randomized game. Open it with your NES Emulator
The Checksum that's also generated is used for generating the same seed again, for example, in races.

Beginning a game:
The goal is the same as it is in regular Dragon Warrior: find the Silver Harp, trade it in for the Staff of Rain, find the Stones of Sunlight and Erdrick's Token, and defeat the Dragonlord.
Along the way, you'll need to pick up Erdrick's Armor, most likely need Erdrick's Sword, and acquire enough HP, MP and Attack Power.
However, all the chests have been randomized, as well as the search spots in Kol, Hauksness and the coordinates.