One-on-One Gaming Rules!
My very first introduction to gaming (Basic D&D, of course) was one-on-one, as I lived in a small village with only one other gamer within 5 miles. As time went by, I found groups to game with, but I always kept a special fondness for the single player game; in fact I still run such a game today.
Now others have made some important and salient points about the focussing of the game and on the role of a support NPC. I wanted to add that on that point, I have always found it really important to try and get the solo player and the supporting NPC to become fast friends. If you can manage that (and I've had it where they ended up lovers!) then you make your life as a DM much easier. At the least you get to be able to make useful suggestions that the player might heed, and you also create an inherent hook which can be exloited to generate dilemmas and motivations (not just the 'NPC abducted route', but giving the PC a different perspective on moral questions, or responsibilites).
But there's another point I want to make: it is hard work to DM a solo game, and it is hard work playing in one. I am not trying to put you off, quite the opposite as I think one-on-one gaming can be truly creative and fantsatically rewarding. But you must remember that there is no-one else to bounce ideas off for the player, no-one to tkae over in teh lead slot for a while when you are stumped or tired. And for the DM, you are their only contact point in the game; you can't sit back and think or rest for a while whilst the players all discuss a problem. The solution I fnd for myself when I DM a one-on-one game is to take periodic breaks (I go and make a coffee), which gives me time to think and take a short break. Likewise, be prepared to cut your player some slack and let them sit back and cogitate for a while if they are clearly having difficulties. Work together and you can overcome this difficulty inherent in the set-up.
Finally, the advantage of a single PC is that you can really role-play intensively. In a multi-player game, you have to make compromises as a DM, making sure that one PC doesn't hog the spotlight and overwhelm the others. Well, now there is only one PC, so you can afford to spend time on the NPC interactions that you'd normally truncate. If you're prepared for it as DM, then let the PC chat with people, bringing in plots and clues through general conversation rather than speciifcally directed NPC clues. I am not sure if I am making myself clear here, unfortunately. What I mean is you can do the ordinary chatting that we in real life do in order to get to know people or to get their impressions of things or just to pass the time. By doing this in-game you make the NPCs more solid and the campaign setting too. Demonstrate how the fantastical fits into the world, the role of Clerics say, not by just telling the player as DM, but by showing the thoughts of NPCs in casual conversation. I know it sounds hard work, and it does like all skills take practise. But the solo players I have had have always liked the campaigns I have run for them because ther feel there is a depth there and a solid cast of NPCs to make it feel real. Sorry if that sounds like I am blowing my own trumpet but I am always happiest with this set-up.
Now, of course, you'll work out your own way with you player to make the game work, but I wanted you to get some feel for what you can try and achieve.
