I've recently had the opportunity to introduce someone to D&D that knew next to nothing about it. One of the first things I did was to toss most of the rules. She said she wanted to play a wizard just out of school. So I gave her a piece of paper with the 6 basic stats, HP, AC, her weapons, 3 spells, and equipment.
Without a plan, I dropped her down in a city and told her there was a tavern keeper that was having trouble with a thing in the basement. Investigating, it turned out to be some sort of slime creature that she blasted with her firebolt spell from the stairs, rather than going down to face it up close.
Then she heard about a haunted house that needed cleaning out before the new owners could move in. Turns out it was owned by an evil old guy who didn't want to die cause he didn't want to go to hell, so he’d summoned a demon to gain immortality. The demon wanted to be released, and to take the damned soul with him. Feeling a surprising amount of empathy for the damned man (who was a ghoul) she decides to sign a contract with the demon, freeing the ghoul’s soul to go to purgatory. In exchange, her soul will be damned until/unless she retrieves 99 souls that escaped from hell. Everyone walks away happy, and she collects her reward for getting rid of the undead monster haunting the house.
The next day the demon showed up to her room at the inn and told her where one of the damned souls was. A nearby bathhouse had suffered a series of mysterious murders. The owner wanted to keep it all quiet, but 3 murders in 3 days…. Investigating the bathhouse, she came across a demon hunter (Paladin) who I had thought might become a companion in her quest. The demon hunter was there for the same reason she was, but she was having none of it. So she fights the Damned Soul on her own in a locked private room.
Thankfully the walls weren't very thick, and as she gets taken down the demon hunter bursts through the door, and takes out the “demon”. The natural form of the damned souls is that of a large grub with a mewling human face. Hardly demonic, and the demon hunter is willing to let her take it for "disposal."
After recovering from her fight in the bathhouse, the demon shows up to collect the soul and to take her to the city of doors, since not all the damned souls will come to her little po-dunk world! A little bit of Sigil, mixed heavily with the market dimension of the M.Y.T.H. series. Her demon doesn't have a lead in the next damned soul, so she goes shopping and finds a “soul trap” for sale, but for more than she has in cash. She finds an alchemist who’s looking for basilisk horn, and willing to pay good coin for it. He opens a door to another dimension, and she goes hunting…
Hunting the Basilisk in it’s lair isn't too hard when you set a trap for it at the entrance to it’s lair! Setting herself up in a good sniper position, she blinds the beast with a spell, and then alternatively freezes and burns it to death. Sawing off the horn, she returns to the door, hands over the horn, collects her gold, and buys her trap.
Each of these sessions has lasted about an hour, and the rules have been kept to a bare minimum, retaining only the most core elements of D&D: d20 to hit, roll for damage, mostly limited spells (5th edition sort of way with cantrips), and have bumped her level just about every session. Progress will slow at this point to a level after 2 sessions, then after 3, then 4. She keeps wanting to play more, so I must be doing something right... Plus she’s interested in trying out a game at the local game day!