I use one tool with an adze and one with a hammer. In the case of extreme ice climbing such as vertical waterfall ice, I carry a third tool to use while placing protection and as a backup in the event that one of my primary tools breaks. I fit each tool with a lanyard so that they can hang from my wrists instead of having to grip the shafts. Basically this reduces arm pump. Some folks like leashing one of their tools to their harness for extra security, but this can hinder smooth tool placement if the length of the leash is too short.
Crampons are the most vital link in the system and require special care on a continual basis.
Learn proper crampon adjustment, and keep the points sharp. I prefer rigid crampons over adjustable ones. Rigid crampons tend not to shatter the ice as much, and they provide more secure placements. Be sure to keep crampon points sharp. A helmet is especially important, as falling ice and debris are common.