You can't play D&D with only one player. FALSE! - Here's how...

"You can't play Dungeons & Dragons with a single player character, it is designed for 3-5 players!" - Well, most official modules or examples in the DMG are designed for a party size of about four players or so, true. However, it is a common misconception that you got to have a large group. One Dungeon Master and one Player is all you need. However, there are a few things to consider...

Playing Dungeons & Dragons with a single player

Do you want to play D&D, but you are struggling to find enough people for "decent" group? Don't worry about it, all you need is two people! I think it even is beneficial to start with a very small group to familiarize yourself with the game because it can be a little overwhelming at first. In a very small group, however, with people you feel comfortable to be around, who are just as eager and excited to play the game as you, it is very rewarding and fun to explore the vast world of Dungeons & Dragons. There is no need to wait, just start playing!

Before I head specifically into the 1on1 experience, here is a brief outline of my history with the game. I am not a very experienced D&D player myself. I started playing, as of writing this text, about one and a half years ago. We started with a group of five people, but in that constellation, we never got past our first session. Two of the players, despite enjoying that particular evening, were not very motivated to go on... Fast forward a few months: We got together another group and played a few games, with me as the Dungeon Master, until the characters were 3rd level, approaching level 4. But, you guessed it, the group fell apart again, this time largely due to time-management issues. We just didn't find enough dates where everyone was available and the time between sessions got larger and larger, so we just lost sight of our adventure... Fast forward a few months again: I am playing regularly with a group of just three people and we are taking turns DM'ing, playing kind of in an "episodic" fashion, but still with an overarching storyline that we shape together. And recently I started a 1 on 1 campaign, with me as the Dungeon Master and only a single player.

My experience DM'ing a 1on1 D&D adventure

Note: This is kind of a work in progress and I will continue to update this and the following sections regularly as I play more and more solo Dungeons & Dragons.

You can check out exactly how my first 1on1 Dungeons & Dragons campaign played out here: The Adventures of Amber Oakwood
This is a list with YouTube Videos for all the adventures of the campaign, including all the resources that I have put together beforehand, similar to a small module description.

TODO: write stuff

Useful tips when playing with a solo character

Here are some things that I think you should keep in mind and can help you have a better time when playing 1on1 Dungeons and Dragons.

Don't give your player a bunch of NPCs 

It might be tempting to simply give your one player multiple characters to control in order to emulate a "regular" group or control them yourself as the DM. But I think this is a bad idea. It is too overwhelming and you can't really focus on any of the characters. That doesn't mean the character can't team up with other characters from time to time when they meet them in the game, but (in a 1on1 session especially) you should always...

Focus on the player

You only have one player, so you should make the story (and the gameplay) all about them. Get the player really invested in their character and also keep an eye on what they like to do. Do they prefer combat, riddles, stories, a good mixture of everything? Also, incorporate their race, class, background, etc into the game. An Orc fighter will require a very different approach to the adventure design as opposed to an Elven mage, for example. Keep all these things in mind when creating the adventure. While this is true for every game of D&D, I think it is especially important with only a single character. And that is a good thing. You can really personalize the experience and get the most out of it, whereas in a larger group you always have to choose a middle ground for all the players.

Let the player decide their own quests

This is similar to what I have just mentioned above, but I want to highlight that you shouldn't enforce any actions or narratives on the player that he or she isn't interested in. Playing custom campaigns in a 1on1 scenario will give you the opportunity to make the player really feel free in the game-world, much more than in a video game (duh), a larger group or premade modules. After the first session, just see how it ended and ask the player: "What do you plan to do next?" - then build the next session around that. Don't plan too far ahead.

A single character is very vulnerable

Especially at the very beginning, the whole adventure might come to a sudden halt when your one character drops to 0 HP. Keep in mind that a solo character dies a LOT easier than even a group of two because you can't just throw in an emergency heal, for example, when a character goes down. I do like my adventures challenging and I think it is very beneficial for immersion in the world when the danger feels real and permanent death is not ruled out, but you should probably keep some (reasonable!) last-resorts at the ready that allow the player to barely cheat death if need be.

TL;DR

Playing Dungeons and Dragons with a single PC is definitely a worthwhile experience and not just a less-than-ideal workaround when you can't find a "regular" group. Just really focus on the player and experience an awesome story with an amount of freedom and personality that is very difficult to achieve in a larger group.