Here's a basic guide showing the common issues in Vectoring MLP Characters.
Here as a list again: Fills not reaching or going outside their outlines; Ears having pointy tips (should be rounded, the only exceptions are Luna, Soarin and Mrs. Cake); Bad colours (in most cases, you can check them on our colour guide, which is linked on the left side of the group's main page: mlp-vectorclub.minus.com/mbiv9… ) Lack of proper tapers; Corners being cut off due to a low miter limit; Stroke width being inconsistent throughout the individual parts of the vector (the only exception is when the artist attempted to create a feeling of perspective); Outlines being too thin or too thick in the vector overall; Strokes being wobbly; Missing nostrils, eye highlights (two stripes of colour on the iris) or eye reflections (white circles); Legs in the background lacking a darker fill; Layering issues (objects being incorrectly layered under or over something), includes eyelashes from the far eye in the 3/4 view being layered under the head stroke; Inclusion of raster elements (all submissions must be 100% vector); Lack of downloadable source (vector) files (only necessary for show traces); PNG image not being downloadable or having a resolution smaller than 3k pixels wide or tall; Exporting image with a white background. Using Program Tracing to convert image to Vector.
Update: 14/04/13 - Added Soarin to the exception on having pointy ears. Update: 29/08/13 - Added Mrs. Cake to the exception on having pointy ears.
It depends on how you want it. In general, you will need a Vector Graphics Program like Adobe Illustrator or Inkscape. They allow you to save in native vector files (AI and SVG) as well as export your vector art in general image files like PNG and JPEG. Do remember that these image files are not vectors, but exported images of Vectors. Simple guide on the differences fav.me/d5ceywa
For Deviantart submissions, I create a zip file/folder with the vector file - AI (Adobe Illustrator files) or SVGs (Scale Vector Graphic files) inside the folder. When uploading the zip file, DA will ask for a preview image. Make sure to allow download. Once everything is done and submitted.
Hey look someone that realizes that a png is a raster and not a vector image. I get so upset when I'm looking for things and it says VECTOR but the download is a png and it's like no. Then people ask me if I do vector requests and it's like no all mine are PNG's, they aren't vectors. I'm working on doing them fully vector but I usually only do my lines in AI.