What's this? I uploaded that dewott picture to tumblr and people seemed to like it and I was asked if I could make a tutorial about this style. I think I was asked the same way back when I used this style the first time. Eek! Well, better late than never. So, here is s little warm up before those bigger tutorials I were promising.
This is my third tutorial and I hope I made it clear and simple enough to follow. English is not my first language so let me know if you see any bad mistakes.
ProgramI used photoshop CS5. These should work in older and of course in newer versions. As for other programs such as SAI, I can't help you, sorry.
HalftonesThis is NOT the only way to make halftones in photoshop but it's my favourite way. It does require you to be in grayscale mode (otherwise results are VERY bright colorful dots) but it doesn't bug me too much (especially if you are making a black/white picture like here). You can also make halftones with a filter effect (Filter>Sketch>halftone pattern) or playing in bitmap mode (that's a bit more complicated. I recommend to look halftone tutorials if you are interested in it.) And do note that smaller the final resized picture, the harder the dots are to see so keep that in mind when you think what size you want them to be.
TexturesUse 'em! About 99% of my textures are from CGTextures,
[link] . They have excellent selection of various textures. AND FOR FREE! You only need to register on site but it's free and I have NEVER got any Email spam from them. There is also 15Mb download limit per day but I've never ran out of that either.
Speed linesThe trick I showed you here is something I learned recently thanks to this very helpful tutorial,
[link]GO AND CHECK IT! It has more about how to create that dot brush and more tips and tricks on how to make different speed lines! Very useful!
If you have any questions, feel free to ask. I'll do my best to answer.

My last tip is of course to read manga to see what kind of shading and style are commonly used in them. And if you do make something with the help of this, feel free to send me a link in comments! I would love to see.

Thanks for reading and hopefully this was somewhat useful.
For the line art part for Cacturne I think the line, "The sketch as your guide, draw the line art." could be improved as "With the sketch as your guide, draw the line art." It's nothing drastic, but it just stood out to me as odd.
Anyway, thanks for the tutorial and shedding more of your helpful tips (and that other person's speed lines) on Photoshop in simple and easy to understand presentation.