I actually managed to see an episode of Red Dwarf being filmed (Siliconia, series 12 episode 2). This is a pretty effects-heavy episode, at least with various characters having the Kryten/mechanoid make-up applied.
The standard Red Dwarf studio set for series 12 consisted of the bunk room, some corridor sets (including one going behind the bunk room and guest set, out of view of the audience), a "guest" set (which changes from episode to episode) or the science room, and Starbug. In our case there was also another set in the corner which was built upon and changed.
The episode takes place on a ship populated by mechanoids, for which a large amount of make-up is required, and our heroes get transformed into mechanoids too. In order to film this, there was a large amount of extras there wearing the mechanoid make-up, but the heroes are in their traditional outfits/look. For the scenes where they are in their mechanoid bodies, these were recorded beforehand and shown to the audience on large monitors (which show all the action being filmed anyway, in case audience members cannot see - I had a large camera assembly in front of me, for instance, so couldn't see much of the action). The scene where the heroes are transformed into mechanoids was filmed a few times live, and the counterpart where their mechanoid bodies revealed recorded a few times, in order to get the best reactions to both, where I assume they used split screen techniques in order to get the desired results.
For space shots, we were shown storyboards and had various stand-ins (the Death Star sporting a Divadroid logo was a popular one), or in the case of Lister's guitar floating through space, a greyscale CG render. Other things are applied afterwards - there is an out-take from a previous episode (series 4's Meltdown) where Lister (Craig Charles) knocks on a wall, pretending it to be stone. From the sound it is quite obviously wood and he explains to the audience that "they were going to sort that out in the dub".