Okay, I'm going to *try* and help without screen shots.
First, Don't draw on the background layer. After you unlock it, you actually have the ABILITY to draw on it, but if you mess up YOU'RE SCREWED. If you draw over your line, that line is gone. You can't get it back easily if you can't edit>undo anymore.
Cell shading is what I call, 'lazy shading'. Almost all anime you see on TV is cell shaded. What I mean by this is, there are three colors per object. For skin, there is a defined line between light, medium and dark
http://upload.wikimedia.org/wikipedia/commons/b/b7/Toon-shader.jpg
in the above pic, the picture on the right is lazy shaded. It has a definite area that is light and dark. the pic on the left side is 'rendered'. Fine art is done that way most often. The more realistic it looks and the more smooth the transition is, the less cell shaded it is.
Multiply can be in the context of coloring, lighting or layer styles, I'm not sure what your confused about, so you can either send me an e-mail later or maybe you won't be confused after I explain basic coloring of anime.
First the scan!
Check your scanner settings and make sure the resolution is 300 or higher. 600 is my personal preference. Resolution will make the image scan more pixels from your page which will get all the little details in your picture. I use 600 because I usually shrink my images after I color them to make them look fancier. Other details are more scanner-specific like where it opens, etc. One important thing though, pick which mode you scan in everytime! whether it's grayscale, RGB or whatever, make sure you know what it's scanning in because that will control how you can color it.
Onto photoshop! I scan straight into photoshop by using file>import>episonstylusC120. The last part is my scanner. Your scanner might not be connected or compatible with Photoshop, so you have to check that. All else fails, just file>place the pic into a new document and save it under a new name.
I'm assuming you know how to trace with your tablet, and I recommend you make a new layer on top of your picture just for tracing. I do this because if I happen to scribble out a line because my brush was too thick, I haven't lost the line, I'm just gonna erase and go back with a smaller brush.
after you trace to your heart's content, hide the picture you scanned by clicked the little eye (while on the layer) that is at the top of the layers bar.
For coloring;
There are many tutorial websites and if you go on deviantart.com, you can find many that may help, but you need to know what style you will color in first.
Two major styles are; cell shading(explained above) and rendering. Both are fine for anime, but I like rendering better.
But first, a word about layers. Layers are like see-through paper you can draw on and stack on top of each other to make a final picture. If you drew a person wearing pants on one layer and, in the same spot, a skirt in another layer, the layer on top would be showing, only. If you removed the higher-up pants layer, the skirt would be visible. The fact that you can completely remove or alter only a specific part of a picture is invaluable. Just image you take a picture and the person is on one layer, and their pimples are on another, wouldn't it be wonderful if you could remove just the pimples without putting white spots/transparent areas all over the person? That's what layers let you do if you set them up correctly.
So onto coloring! Cell shading is focused on selections. so lock your trace layer and make a new layer on top for each color, that way if you mess up or want to change a color, you click that layer and go to town without risking the great job you did before on other colors.
Many cell shaders use the magic wand to select and area capture by your lines, and then they use the paint bucket to fill it in. Then later they make selections with the lasso tool for shading that isn't captured by lines (there isn't a line for where the dark/light starts)
That process is actually faster for most, but rendering produces a more beautiful piece.
To render, you would still make a new layer for your colors, but layers for shading/lighting are all on one, and they blend in the colors with a brush. That method is basically the same as real life mediums, so if you can paint, you can render!
If you need more help, you can send me an email and I'll either explain or give screen shots. I'm currently in school for Game Art and design so I actually study this stuff! ^__^