Just to add to what Snowblizz said:
Washing uses an "ink" (pigment suspended in a watery substance, rather than pigment in the much thicker paint form) and gives a slight tint to raised areas, but mainly collects in recesses to shade them. The other example of where they're most useful is hair and fur - paint it a mid-brown, give it a coat with brown wash and you get good instant shading for your rank and file.
While I don't see the point of the Foundation paints most of the time (I may only be 26, but I'm an "old timer" who remembers Warhammer 4th and 40K 2nd edition!), some of the old yellows were a bit thin. GW claimed it was something to do with the old manufacturing process and that the paints couldn't be improved (hence the move from the old hexagonal pots from Coat d'Arms to the newer dumpy screw-top and then dumpy flip-top pots) and colours like Bad Moon Yellow really did have to go over a clean white base, but I never had a problem with rest of the range. It'll probably depend on style and preference - some people will swear by the new foundation paints, while some people will just see them as GW making another quick buck (after all, Rackham can make a wonderfully thick black paint that is cheaper than the Citadel one for a larger pot, and it waters down for normal use very nicely).
Washes do generally work best when done in a colour similar to the base (brown or chestnut wash over browns, black over blacks and greys, blue over blues, etc) but sometimes you can achieve other effects by using them differently. Browns over metal make it look rusted and mistreated (undead, Orks etc), blues over metal give it an almost ethereal feel (high elves), a thin green over Wood Elf armour can tie together the "natural" feel (if done right), and shades of purple and other colours can be used on skin to get all sorts of alien effects (purple around the eyes of a vampire was a good one I saw, but an advanced technique to get just right so that he isn't wearing eye shadow!)
With regard metal and why it works best over black, I think it is all about light. A black undercoat below metal gives the shiny silver particles a good base to contrast against (since the silver paint is a mix of grey and silver), where as a white undercoat is too light and doesn't let the shine stand out. TBH, I think I might have done some of my later High Elves in silver over white and used a thinned mix of armour and blue wash and got an effect that I was quite happy with. It wouldn't work as well for most other armies, but I think my elves worked quite well without black for the metal.
I agree with Snowblizz's recommendation - get hold of the How to Paint Citadel Miniatures book and give it a read (
Wayland Games have it at nearly 20% off, and we get a referral fee as well). Also, if you can get into a local Games Workshop store then the staff will be able to give you some pointers. I think GW are putting more and more bits up on their website as well these days in terms of hobby articles.