I was really agrivated to see how many people thought it was good. I didn't finish watching. I would have stopped sooner if I didn't see the YouTube comments of "yay, Derpy!" and watched until that part. There was no substance. Just pandering.
Whoa! No one's asked me for a tutorial before! Unfortunately I don't, but I can tell you what I know.
First off, I use Inkscape. It's free and pretty powerful. Second, I use the bezier tool for everything. Click out a rough outline and then bend it by dragging from the middle of the line. It helps to change the node type a bunch, so certain nodes are angular and others bendy. Lines can be changed to fills so you can adjust the edges of them, but will mess up your colours if you don't do them soon enough. (Go to the toolbar->path->stroke to path) The fill tool is really handy, but as far as I know, will fill for ALL the layers. You may need to hide some to get it to work. Then press the key 'Pg dn' to get the fill to the bottom of the other shapes. The eyedropper tool only works for fills, not outlines. Watch your layers! Layers work similar to any other drawing program, but within each layer you can also click a shape and press 'pg up' and 'pg dn' to make it show above or below other shapes. As for gradients like in the Derpy, I honestly have no way to describe it. That was brand new to me. This tutorial got me started and will probably be your best help: [link] (It's illustrator, but works for Inkscape too). DeviantART has even more. The vector club has a bunch in it's folders: [link]
I'm terribly bad at explaining it so quickly, but I hope I gave you any help at all.
Remember that most of it really is experimentation and practice. It seems tough, but it's easy to get a handle on it if you think about it the right way.
I would love to see a version of this based on Dash saving Soarins pie. I wonder if Soarin buys a pie just to see if a cute Pony will take the challenge to save it when he drops it near them,such a cute stud.
I hope you don't mind me saying this but the drawing could use some more work. Technically this a great piece of art but lots of small flaws stick out. First of all the hair doesn't really look like hair but rather some kind of clay model attached to the head, especially since you put a thin dark line between the hair and the head itself. It should be the other way around, with head color mixing in with hair color, preferably by doing thin short line strokes. Actually whole hair should be done that way, with thin line strokes to make it look like real hair - it would fit this style. Also on the subject of the head, you should not be able to see her right ear from this point of view - her left ear is correctly placed at the back of her head, while the right ear looks like coming out of her head somewhere in the middle. The jaw line should end a bit sooner (not going all the way to the back of the head) as it makes neck look a bit detached from the head. Finally, the worst part in my opinion is the wing. If I hadn't now about MLP I would definitely not recognize this as a wing at all. Considering the style you are using I would suggest drawing something more realistic, referencing actual wings.
By the way, the text is quite hard to read (maybe it is the font?), it is missing something that would make it pop, but I am not really sure what can be done with that, maybe some outlines could help.
I guess the only thing that seems 'off' is the text style. It looks great, but the typed text makes it seem...unfinished..i dont know. Im not trying to say it was bad, just maybe if the words were painted on, it would be more realistic..i guess.
Sorry if i couldnt explain it well enough. Still faved!