The champion spotlights actually cover a lot of the basics and tricks to any champions you're interested in. Other than that the best thing to do is to watch people better than you play, and then do what they do. The more involved stuff (wave control, freezing, optimal trades, buffering inputs, zoning, split pushing,
DEALING WITH TILT) is a biiiiiit more specific.
FoxDrop can give you some good advice for jungling,
This guy is kind of perky but has some good vids on creep control,
imaqtpie is always good for picking up some adc mechanics, same goes for
gosu, etc. etc.
If you want barebones basics, the thing to do is look up some champion guides and start from there (
player made guides -
statistical builds - Never fucking go on Mobafire). Best case scenario, you have someone who's already into League explain what all the numbers and shit on the screen mean, ap, ad, mr, crits, armor, you get the idea. Other than that, get in game, lose a shitload, get yelled at by your team, and then learn what not to do until you eventually find what works. Shit sucks but eventually, unless you have the cognitive functions of a fourth grader, you'll be able to pull yourself out of silver elo and start having some "enjoyable" games.