This is not a do this, then do this, then do this type of logo design tutorial. Instead, discover (or rediscover) ways to use simple shapes in logo design and creating other custom graphics.
Examples throughout this article are done in CorelDRAW, a vector drawing program. They utilize only the most basic tools — no fancy filters, fills, or complex manipulations. You can add filters and special effects later after you've got the basic design worked out. Look for the simple shapes that make up each graphic illustration or logo design.