You are right, Everything is easier on a computer. However when it comes to analogue equipment there are limits since we're not exactly dealing with binary codes, thus a 4 channel mixer can actually take you quite a long way. Dubbing on a computer has its benefits, since it's easier to control, you can take the skills to a next level.
The idea of old school dubbing is to have a multitrack recording of whatever it is you want to dub (whether it is of yours or someone else's work) then to optimise the sound levels. You need a mulitrack player that can play the recording you want such as the TEAC or the Tascam (http://en.wikipedia.org/wiki/Multitrack_recording
), which has seperate outputs that you input into your mixer. Or you can lead them through into different effects and then into your mixers, it's up to how you want to handle the separate tracks. Each track will have an individual line of sound, for example, one track could have the drums, one could have the vocals, one could have the bass etc etc. However, it is really a mixture of how the all-over sounds were recorded and how you chose to distribute the sounds into the mixer.
Once you have everything setup and optimised, then the fun begins and you can play the mulitrack and live mix the different levels. For example, you could lower the guitars and louden the vocals, cut them off at certain points and add reverb and echo effects in order to give it a ping-pongy trippy trail. You could give the bass more power by upping the lower frequencies on that individual track. You can get rid of some of the upper sound frequencies on the drums to give it a more thumpy feel since all that's left is pretty much the kicks and the snares- this is more of a Hip Hop tactic but it's quite powerful when you want people to feel the rhythm and bass. Also, stripping tracks off certain frequencies makes the overall sound more sparse and more leeway for you to bring out certain aspects of what you love into the gap that you've created- this is where people will focus and fall into a blissful spiral.
This is the technical essence of dub.