Before launching into this, I'll just make clear that this is what I do, and not necessarily what everyone does or would recommend.
Tools and Materials
A good modelling knife ( I use an X-Acto). Modelling files - available in packs. Fast-acting Superglue (preferably with a way to apply it in small amounts (I use Zap-a-gap). Polystyrene cement (preferably with a brush applicator) if you are putting together plastic minis. PVA Glue - for applying basing. Flock/sand/rubble - your taste as to how you want the base to look.
Don't buy GW's brushes - you can get similar brushes from an art shop. Look for sable brushes; you could use synthetic, but I find sable gives more "feedback" to my hands and eye than synthetic brushes do, allowing me to control the brush better. If you want to be fancy, you can look at Windsor & Newton Series 7 brushes, but you don't need them to start off with. They are excellent though.
Acrylics all the way. They are just much easier than oils and enamels. They dry faster (not always a good thing but see later), are water soluble when wet, and are (in the main) non-toxic. A large variety of manufacturers produce paint these days, and it's one of the few areas in which I go for GW/Citadel. Their Wash range and range are suberb. In fact, you could get away with just buying those two box sets.
ALWAYS prep - I can't emphasise this enough. The difference it makes to the finished model is aesthetically huge. For plastic minis use your knife to gently scrape away the mould lines. Plastic minis these days have come on leaps and bounds from even 5 years ago, so you still need to take care not to get rid of detail. For metal minis, you can use your knife and a file. I can't speak for the new-fangled plastic-resin or whatever that Mantic and GW are using, but I should imagine that the old techniques still work but you may need to fill in the moulding bubbles with green stuff.
There is so much variation in how people go about doing this stage. It really depends on what effect you are after, how much time you want to take, and how many models you're painting (see below). There are three main colours for undercoating (well there are lots but to begin with we'll say 3): black, white, grey. I have used all 3 and like the effects they all give.
Black - Pro - gives strong definition of areas of the mini and adds depth of shading (no need to blackline). Con - you need to carefully layer colours on top thinly in order to get strong colours. Suitable for any mini but works well for dark colourschemes or 'sinister' minis.
White - Pro - good strong colours. Con - areas you miss are really obvious! Suitable for any mini but most suitable for colourful ones or 'goodies'.
Grey - Pro - Provides a good base for either type of scheme, especially in combination with a dark wash (black/brown) either before or after applying base colours to areas. Con - I haven't really found any.
Applying the Undercoat
A matter of time/preference. You can either apply by brush or spray. If you're spraying, you need to be seen by a vet. OK, seriously, on the matter of spray - don't buy GW/Citadel's (notice a theme?), get car-body spray. I get all of mine that way and they are cheaper, contain more and give better coverage. Spray outside in low humidity when possible.
Are you wanting to paint an individual model as best you can or are you looking to paint batches of models at the same time to acceptable standard? The same disciplines apply but they require different mindsets. More in another post, perhaps.
A base completes the model. If you leave the base blank, to me it looks unfinished and ruins the overall effect. Even if it's a coating of flock, at least it's something.
Like undercoating, varnish can either be brushed or sprayed. It comes in gloss or matt and most people recommend a first coat of gloss (protects well) followed by a coat of matt (makes it less shiny). You can then either leave the metallic parts and gems shiny or redo them with gloss if you've hit them with matt. Or just leave them matt if you like that effect.
This is a really basic overview, but if people want more information on something, I can post further on specific topics...