My girlfriend and I have the Dungeons & Dragons Basic Rules Set 1, Expert Rule Book, and Game Adventure Book. We're looking for free two-player adventures which we could run by ourselves. We'd like them to be simple and straight-forward, as we are beginners. How can I go about finding this kind of adventure?
It is a problem that Lost Mines of Phandelver is designed for 3-5 player characters (PCs), plus a DM. I'm playing Phandelver at the moment with a group. One session only two players turned up, and I discovered how deadly this could be with no modification. With one PC and no modification, you would likely not last past the first encounter. As far as I can see it, you have options:
1) Tone down Lost Mines of Phandelver
By 'tone down' I mean reduce the level of the encounters. This will be easier near the beginning (where you could just reduce the number of goblins), and more difficult as the game progresses.
I actually did this with the session in question - they were supposed to encounter 6 hobgoblins (rolling on the random encounter table at that point in the game), but I cut it down to two.
With bigger monsters it is more difficult, though you could 'wound' them, reducing their HP (hit points) and possibly some of their special abilites, and XP (experience points) commesurately, but that can get complicated and possibly lack verisimilitude, so there is always option 2).
I didn't do this to one monster (a grick) and both characters ended the session unconscious. Oops.
2) Play Phandelver, but have your girlfriend control two or more characters, and/or bolster the party with an NPC or two
In this solution, you can still play Lost Mines of Phandelver, but you could split the party between you and your girlfriend, with your girlfriend controlling two PCs and you controlling another two (or three if you want to use all five) as NPCs (non player characters - controlled by the DM).
This obviously has the disadvantage of complexity, but it can be fun nevertheless, and gives you and your girlfriend an idea of the different types of characters avaiable to play.
You could also combine 1 & 2 in the following way:
3) Start Phandelver with two (N)PCs, tone things down at the beginning, then add (N)PCs and enemies as you gain confidence
For example, your girlfriend could control one PC, and you one supporting NPC (just choose two from the pregenerated characters).
Spoiler, in case your girlfriend's reading :-)
Cut all encounters in half - so two goblins on the road, half the numbers of goblins in the cave, and either weaken the bugbear in Cragmaw Hideout and/or take his wolf away. Don't forget to halve the XP. Then at the end of Cragmaw Hideout, take Sildar Hallwinter with you and have him stay as a friendly (and tough) NPC. This presumes that your girlfriend will choose to go to Cragmaw Hideout first, but that is the most likely course of action, and you can always guide her back there from Phandalin if she goes there first.
Then as your girlfriend gains confidence playing, she could start to control another PC, and so you will have a tough enough party to face the later more challenging stuff without cutting things down.
For options 1-3 I strongly suggest you have a cleric in your party - parties with clerics last longer!
I haven't tried this myself, but for options 1-3 you might also want to read Play it Solo:Dungeons & Dragons Starter Set. Although it is geared to playing completely solo, looks like it might have some useful advice for converting Phandelver for playing with fewer players.
Or, for something completely different:
4) Find an adventure for one or two players from an earlier edition of D&D and convert it.
This is not my idea, but is described in more detail here:
You might have trouble doing this conversion just with the basic rules though - you would probably need at least the 5e Monster Manual, though I suppose you could just take the idea (and maps) from such an adventure and swap in monsters from the Starter Set.
First, let me congratulate you: you're having the problem that your players are having too much fun. As an inexperienced GM, this is the best problem you can possibly have, as long as you don't stress yourself about providing the material (don't be afraid to ask for more time).
However, the solution is easier than you seem to think: just tell them beforehand. There's no need to pretend that D&D isn't just a game; you know it and your players know it. You don't have to give away the plot just to say "Hey everyone, I'll be running a one-shot tonight." All they know is that the plot will be wrapped up by the end of the night (if things go well). There's no need to give them the false sense that their adventure might continue on if you have no desire to do so. Indeed, it's definitely worse to be disappointed that a story you liked suddenly ended than to know a story you haven't unravelled yet is going to end by tonight.
That said, please feel free to expand upon your one-shots. There's several different ways to DM, but I personally prefer to write what's happening next between sessions, not plan out the entire campaign in advance (although I will think of some good ideas on where to go next, I won't decide until later). If your players really liked one of your one-shots, there's no reason you can't make it into a real campaign, even if you never planned on it -- tons of campaigns happened this way. And you certainly don't need to write up your entire campaign as a module for it to be "valid" or even quite good.