You don't have to remove the strings just loosen each one enough to lift it out of the nut and off the bridge. Clip any hairs that might have developed. I use a little bit of rubbing alcohol and a paper towel to remove the gunk, it also removes built up rosin if that's your thing. Next I use mineral oil and a light kitchen scrubber on the playing length and then wipe everything off really well with a clean paper towel. Bring the string up to tension and play it! Depending on where you live you won't have to oil them every time.
VERY IMPORTANT!! If you use a bow only oil the strings well north of the end of the fingerboard, rosin and oil do not mix!!
An alternative is to use vodka or 'shine, especially if you need to clean your other guts at the same time.