How do you design a meaningful logo quickly? I attempted and this is how it went.

Curve Design:

Start with fast brainstorming of few basic ideas and choose one that seems most appealing.

I used Inkscape to draw some basic handwriting curves.. I have a tablet, and I wanted to incorporate some sort of a "signature" into the design. I used freehand lines, then cleaned its bezier points to get something that's got structure but still looks hand drawn.

Sketching:

Develop your chosen skeleton further...

I then took those basic curves and developed them in Sketchbook further.

Coloring:

Inking:

Last step would be take the skethed and colored logo to Inkscape (or similar software) and produce it as a final product!

You'd want your original version to be a SVG so that it can be arbitrary scaled up or down.