Playback tools
To play back demos recorded with Aurikan's engine, you'll need DosDoom 0.47 or any other port that can play back DosDoom 0.47 lmps.
To play back demos recorded with TASMBF, you'll need (surprise, surprise) MBF.
Both MBF and DosDoom can be found at Doomworld's source ports page.
To play back demos recorded with TASDoom that were not converted to DosDoom/Doom2 format, you'll need TASDoom.
Recording tools
We used two different methods to create our Tool-Assisted Speedruns:
The first, which we recommend for short demos, is using TASDoom. It's simple and very easy to use.
The second, which we recommend for longer demos, is using TASMBF. It's more complicated but much better for long demos.
The zip files contain everything you need including documentation and a tutorial for TASMBF.