In addition to the points-requirement (see LEVELS), a number of quests must be completed before you can be promoted to Apprentice-Wizard. It's a good idea to start thinking about them as soon as possible.
The quests are listed in INFO QLIST.
Some more information can be found with the QLIST and QDONE commands. Note that quests listed as not done, still might be impossible to complete. This is due to the nature of the quests.
Once completed, answers or directions may not be given away to less experienced adventurers, although subtle hints are allowed.
Read the FAQs to get the answers on some of the more frequently asked questions about quests and game play.
Note that some of the quests require you to pit some treasure before you'll get it recognized as completed.