The main thing you will need is some artistic ability -- no matter what tools you use, if you want an original design, you will have to visualize and draw it.
As far as tools, you will need some vector graphics editor and sufficient skills to use it. Common commercial software choices for vector drawing are Adobe Illustrator and CorelDRAW. The only free application of that type that I know of is
Inkscape.
Don't confuse these programs with raster graphics editors, such as Adobe Photoshop and all sorts of Paint-this, Paint-that. Raster graphics are all about bitmaps of fixed size and resolution. Vector graphics are all about lines and shapes, and can be rendered at any size and resolution, without loss of quality.
Commercial printing requires designs in vector format. One can always render a vector graphic to raster at any desired resolution, but not the other way around. If you want your work to be done right and even remotely close to professional standards, you will want to use vector graphics. Creating an original logo using raster graphics might be acceptable only if it is intended exclusively for web use.
