more seriously though, take things slowly and explain fully why things are happening; she won't know the game as well as you do and it might be confusing at first, since different genders usually approach the game fairly differently.
Ok, first off... that quoted bit is just
_wrong_. The last thing this hobby needs is yet another person trying to propagate this. It's also pretty offensive.
_PEOPLE_ are different. How someone approaches rpgs is _not_ a gender issue. My wife for example is just as happy to hack and slash as the next person; she also like story based stuff where she can really get into the roleplay of her character. And she's not above sticking her hands into a bit of min-maxing either.
If you approach teaching rpgs as some sort of a gender thing, you're most likely going to come off as condescending and offensive.
This is one of my few pet peeves.
Now, to answer the OP...
I run one-on-one games for my wife. She's got some experience now, but she's only been really playing for the past 2 years (other than a brief stint back when we were teens).
Here's my advice in no real order:
1. One on one games can be darn tiring.
You don't have a group to help take the load off, being able to think about how something might work out for one character while you're dealing with another. You don't have other players to keep each other entertained while you're setting something up or looking for some other thing. You are _always_ on.
2. Prepare a lot of stuff in advance, but be vague.
You can potentially cover an awful lot of ground, because you as the GM have little down time, and you've got one person focused on doing something. Yes, it means you can have really great and long roleplaying bits, but if she blows past rping something and starts charging somewhere, she's going to be able to potentially cover a lot of ground.
It also means you're going to want to be a lot looser in your preparation because you just don't know which direction she's going to head off in or how far she's going to push.
3. Combat kills
You want to be careful with combat. D&D is geared towards their being 4 people. That means that you're going to have to be careful with the opposition you put up against her. The CR system isn't the horrific train wreck some people make it out to be, but it _is_ something with wriggle room in it, which means things can go pear shaped pretty easy.
The other thing about combat is, a lot of people (and modules) use combat to "fluff out" the game. When you're doing one-on-one play though, unless the other person is into some _serious_ hack and slash, combat gets old _really_ fast, especially at the frequency that a lot of adventures (and people) have for larger groups.
4. Don't create a lot of support NPCs
This is going to go counter to a lot of the advice people offer. They're basically going to say that you should have an entire adventuring party, and it'll be your one player and then a bunch on NPCs.
You a big fan of rolling dice against yourself? You think your player is going to be on the edge of their seat, watching you roll dice against yourself?
Almost anything the NPCs could offer in terms of support (other than simply being another body and therefore having some extra actions) you can get with magic items or something else.
Every NPC that you have hanging out is an NPC that's taking spotlight time from your player.
If your player wants to head into town, become friends with someone and then drag 'em along on the adventure? That's cool. If your player just wants to make a bunch of friends in some town and hang out chatting with 'em, that's cool too. Because it's still about the choices the player is making.
You need healing in the game? Have hit points come back at the rate of 1 per hour.
Give a medallion that will heal 1d6 Hit Points per round. It's got some use for combat, but it'll mean the character doesn't have to worry about travelling back to town after every encounter, having a pack train of animals carrying healing potions, or dragging along some stupid NPC just to be a healing battery.
Need a bit of magic "umph" for combat? Give the player a cool flaming sword, or some nifty armor that shapes itself to the wearer's desires, or whatever. A rod that does a blast of lightning each round. Whatever.
5. Pay attention to what the player pushes for.
When you're running a group, you have to juggle a bunch of people and keep 'em all happy. And they're all willing to give way on what they want/expect since there's other people involved.
When it's just you and one player though, they're going to expect to be able to do what they want to do. Trying to railroad them along on something is going to really backfire in most cases.
6. Let the player shine.
This kind of ties in a bit to #4. You've got one Big Damn Hero to worry about. Be willing to "bend" or "break" the rules. Cool magic gadget that you'd never hand out to a group? Consider it in this case. It's not like it's going to be _hard_ to find opposition for the character, as it's only one character.
Give 'em "mook" versions of things. Instead of going for the full CR of something, just give it a number of "hits" equal to its HD. So for example, that Minotaur with 6d8+12 HD (CR of 4)? It'll take 6 hits and go down. Not 6 HP, 6 Hits. It can still be a nasty opponent, but you've shaved down it's threat.
Want a good brawl? Just give people 1 or two hits, and watch the player get all excited as they strut their stuff.
And when they come up against a "full" version? Give it an impressive description. That way they know this isn't some chump that's going to go down with a casual backhand.
How you describe the opponents, and the effects the player has as they go into combat can really help sell this. Let the player feel like their character is a Big Damn Hero.
And don't tell 'em that you're only using "mook" versions, unless it's something like the minions of a Big Bad Necromancer or something.
