Hey, not sure how new you are to this, so I apologize if some of the info I give here is too basic. Trust me when I say I'm not a great speedrunner by any means, so if anyone else comments with stuff that conflicts any of what I say, I'd advise to trust them.
Recording a demo: I personally like to use the source port prboom-plus. A quick Google search will turn up what you need for pretty much any major downloadable source port. If you use prboom-plus to record a demo, first open your command prompt and prboom-plus folder, then click on the prboom-plus launcher icon (dying marine) and drag it into the command prompt. Hit space. Next, type: -iwad [one of the 4 IWADs].wad -skill [1-5, ranging from I'm Too Young to Die through Nighmare!] -warp [map number you want to play] -complevel [# (use -complevel 2 for Doom 2 based WADs like Alien Vendetta, -complevel 3 for Ultimate Doom based WADs, -complevel 4 for Final Doom based WADs, or -complevel 9 for WADs that use specific Boom-compatible features like SODfinal or Scythe 2)] -file [the PWAD name you want to play].wad (optional -fast if you want to play with fast monsters, -respawn for respawn monsters, -nomonsters for nomo demos) -record [demo name - standard conventions can be looked up for WADs, and it is customary to keep demo names short and sweet, usually 8 characters or less]. You don't have to use this specific order for entering all the commands, but it's the order I personally use.
Example command lines for recording a demo:
-iwad doom2.wad -skill 4 -warp 17 -complevel 9 -file scythe2.wad -respawn -record s217r
The s2 stands for "Scythe 2," the "17" for MAP17, and the "r" for a UV-Respawn demo. After you record a demo you like, you can go to C:/Users/[you] and find s217r (or whatever you named your demo) and drag it to your desktop if you prefer. After the demo is recorded, the time is usually added to the end of the demo name. (For example, say you got a time of 5:42 on your UV-Respawn. You could then change the demo name to s217r542. And there you have it, a demo name that is 8 characters, short and sweet.) I also recommend watching your demo at least once before releasing it to make sure you didn't accidentally record over it or find that you only got 99% kills or something like that.
Now that you have a completed demo, it's a good idea to write a text file (Notepad document) with some basic information about the WAD you played, map(s) you played, run category, time, complevel, etc. You can include comments about the run if you'd like. When you have both the demo and the text file ready, put them in a folder, zip it up, and submit wherever is appropriate on Doomworld. Andy Olivera (who maintains DSDA) should see it, and DSDA gets updated every Monday or so.
If you didn't know any of that previously, I know that's a lot of information. If you have any clarification questions or want to know about other stuff, feel free to reply or PM me and I'll see if I can provide answers. :) Happy speedrunning!