Bic Mark-It markers and Sharpie markers, A.K.A the Poor Stamper's Copics, are perfectly adequate substitutes for the much more expensive Copics. I have two reasons for not committing to the Copics. First, I am an ambivalent colorer. After all the coloring I've done in the past two weeks or so, I will be happy to have at least a few months of rocking and rolling on block stamps before touching another Prisma pencil, marker, or watercolor again.
Second, given my ambivalence to coloring, it's rather shocking the diversity of coloring media I
hoard own. These include watercolors, watercolor pencils, watercolor crayons, Twinkling H2Os, prisma color pencils, Bics, Sharpies, SU markers (the full 48-color set), aqua painter and SU reinkers, and chalk.
Wow. That list is highly embarrassing. But I think it definitely explains my strength of resistance to the allure of Copics. If, unlike me, you enjoy coloring or have lots of money to spend, I will say that, in my admittedly limited experience, Copics work better than Bics or Sharpies, both in blending more easily and in color selection. Perhaps the biggest problem with using these Copic substitutes is that the colors tend to end up being pretty intense. I understand you can get lighter results with Copics. You get what you pay for, but in this case, the cheap substitute will work in a pinch, as long as you're not too picky.
When I bought the Bics and Sharpies, I made a sort of cheat sheet to experiment with blending. It's come in handy for remembering which colors blend better.

Here are some of the combinations I used in today's tutorial. Aren't all the colors pretty?

Below is the method I've pieced together from various blog tutorials and videos and a bit of practice (a very little bit). If you really want to learn how to do this sort of shading, I highly recommend looking for a mentor more confident and experienced than I. But if you're happy with a little knowledge, I'm your woman.
To start, stamp your images in Memento or Palette black ink on PTI white or Gina K deluxe cardstock. I can't tell a difference in the blending on either paper, but the Gina K will not bleed through and is therefore preferred for one-layer cards.
Start coloring by taking the lighter shade and covering the entire area. [Note: the blue butterfly is finished, the green one just has one layer of light green sharpie.]

Then, add an area of the darker shade using small, circular penstrokes.

Go back over the dark and light areas with the light marker, working out from the dark area toward the lighter area. In my experience, this one pass is inadequate to get a really nice blend, so add more dark ink.

Then, go over the whole thing again with the light marker with small circles, repeating until you have the color blend you want. This second pass of the light color should give you a lovely blend.

I repeated this on a bunch of butterflies to make these. I cut one out, thinking to use them as I had used the butterflies from the Twinkling H2O post, but alas, I got lazy.

So I pulled out a 1" square punch and made a very simple grid. Unfortunately, the two gems in the corner are a bit too big, but I like the colorful effect of the butterflies anyway. And see how I used that one butterfly I cut out? Clever, eh?

For this second card, I used Gina K paper (the aqua is PTI) because I wanted to stamp the butterfly directly on the card base. Despite laying down a lot of ink, there is no bleed-through on the inside of the card.

And now you know everything I know about shading with Bics and Sharpies.
Supplies
Stamps: Hero Arts
ink: Memento
paper: PTI white, aqua; Gina K Deluxe white
accessories: rhinestones, markers, punches