I DM'd many systems (including one I wrote myself, and one created by a fellow member of our cabal) and was generally happy that people enjoyed the campaigns I ran - I was often asked to step in at zero notice and continue a campaign when the main DM was ill etc - I just switched my character to an NPC and busked it.
The key (regardless of game systems) is to remember that the DM is narrator in a storytelling game.
Before now I've run session where nobody was allowed dice or paper, and everything went by "feel" - very karmic, but also focused on play rather than "rules lawyering".
I hated playing in games that seemed like they were on rails - I'd just re-draw my mental map on the fly and ensure that if the party went into town instead of through the woods, they'd still meet the creepy guy selling weird stories, or fall into a well or whatever.
The main realisation was when I remembered that we were all together to have a laugh, not to kill X of Y monsters in my carefully created labyrinth. If the team wanted to have a drinking game in a tavern and a fight with the watch, then let them. We can chase dragons next time.
One of the most interesting games I ever came across was Prince Valiant - there are no dice (you toss a few coins, but mainly it's about telling the tale).
EDIT (will automerge): If you really want to learn to GM, get out from behind the rules and play
SLUG or
Fudge.
The entirity of SLUG fits on one sheet of paper, and works in any genre.