The quests button can be useful, it will let you know when you are near a quest item or monster, and you can use that as an early warning system in some places such as nearing Nihlathak in Act Five. Most players have seen all the quests many times and just double click their keyboard hotkey for Quests when the button pops up. As you execute the various steps in the quest, the instructions in the Quest menu will change to tell you what you need do next. Many quests have multiple parts, where you must gather several items and combine them, or take them back to various NPCs to get more information or a new item. The Speech button at the lower right will replay the dialogue you heard from an NPC or read in a book when you first were given the quest. You can always check it for more info if you get lost. The info presented in this box will generally guide you through the quest, telling you just where to go or who to talk to next. If you click it the Quests window will open up with the current quest highlighted, and more info about it in the box at the bottom. There is also a Quests button on the mini-panel pop-up icon strip, and when a Quest is being given, either by an NPC or triggered by you entering an area with one, the Quest Log button will pop up to the lower left of your screen.
To access information about quests, press the “Q” button on your keyboard, or whatever you have changed it to if you’ve custom set your hotkeys.