I think the skills you need as a good speedrunner really boil down to two things: Movement and Memory.
This is probably the main one, and it's a bit tricky to work on as Doom generally doesn't test your movement skills that strenuously. For the most part, the enemies in the game are weaker than you, slower than you, dumber than you, have a much slower fire rate, and what they do fire does less damage than you can deal back to them. And the level layout rarely requires fine movement skills either. You learn to strafe, you learn to run, and that's where the lessons stop. Just adequate movement skills are enough to defeat the original game, and most pwads for that matter. And if that's the case it's hard to keep pushing yourself. And very easy to think you've reached a plateau in your skills when in fact there's a lot further to go.
So two ways around this. First, play a lot of deathmatch. That takes care of the enemy imbalance problem, giving you opponents a class above any you'll find in single player. You'll learn to move well, and fast, as the alternative is getting fragged a lot. Second way is to follow in the footsteps of previous Doom gods. Watch some speedruns, good ones, and try to do the same thing yourself. If they can do it, you can do it. And even if you fail you'll probably learn something about the way they succeeded. Copying old speedruns gives you the opportunity to practice at things the original game never requires of you, like trick jumps or 2-BFG kills or pacifist runs. And that's when you start learning speedrunner tricks for yourself.
There is of course a third method, which is to switch to mouse control, but I never saw the point myself :)
Quite a long time ago I used to learn piano. The way you get good at a particular song is to first read through the printed tune, play it to commit the sequence of notes to your head, then practice, over and over. At first the copy held in your memory will be very weak and tentative, and you'll play slowly so you have time to read and think. Over time your memory becomes surer, and you need the printed music less and less. Eventually your brain is telling the muscles in your fingers to move even while you're still on the previous note. And then it's all in your head and you don't need the music. You don't even need a piano, you could just play the song with fingers in the air.
None of this is learning technique. This is all about grooving things deeply into your memory. You want to know the piece so well you don't even need to think to recall any of it, your fingers just move in sequence and you perform.
Well, that's my metaphor for a what makes a good speedrun. It's really the same thing - you play a route once, see where you have to turn left, where you turn right, where you shoot. You commit the sequence to memory. And then you play it again, and again, and again. Till the sequence of keypresses is second nature, and nothing in the level can surprise you anymore. You know where every monster is in every room you enter, and how they'll react when you run through on your chosen route. You play and play to learn the rhythm of the run, and you can visualize ahead of time everything you need to do. And at some point you stop training for your good run, and start performing it.
There's really no substitute for practice. Some players are quicker to pick up on routes than others, but generally a good speedrun time will take dozens if not hundreds of tries. And yes, some of that is rolling the dice to get luck from the random number generator, but mostly it's just about getting the sequence learnt. And once you've got that, luck tends to fall your way.
TL;DR - learn to move well, and practice heaps.