Depends on your definition of 'best' - fastest? cheapest? most comfortable?
Note this info is based on some quick web searches in Russian - I have not been that far down south myself!

There is a daily intercity train Moscow-Nalchik which stops at Mineralnye Vody and an elektrichka local train which does the Nalchik-Mineralnye Vody line. Both appear to take about the same amount of time (about 3.5 h), the elektrichka will be cheaper but less comfortable, on the other hand times are quite good (afternoon into Nalchik arriving 1730, morning out of Nalchik departing 0741).

There are no doubt buses and mikroavtobusy between the two towns - could not find any avtovokzal timetables through. I tend to stick to trains in Russia unless trains are not an option or they are the comfy modern coaches you sometimes get. If you are staying at a skiing resort they may offer transfers from Mineralnye Vody. There are also private taxis which will be the most expensive but probably fastest. However I don't know how or if weather conditions affect road transport at certain times of year.

Hope that helps a bit!