The most basic skill any logo designer is expected to have is using the software of designers. The industry standard is "Adobe InDesign." Although it is acceptable to use other software, this is the most commonly used. It can do everything from sketching out rough line art to a fully finished logo. It is consistently updated and is made to be intuitive. Most design companies will expect that applicants know this software. Typically, only freelance artists consider using a different software.
A logo designer will be expected to have basic drawing skills. Although software can be used to augment the drawings, a designer must be able to show the client a rough outline of the logo during a meeting. Drawing can also be the easiest way to create the skeleton of a design. Many softwares can also accept direct drawing input on a pad or can use a scanned image to start the digital aspect of the process.
Clients have many wishes, but many do not speak design language. A crucial part of the logo designer's job is to listen to what the clients say and hear what they want. These are not always the same thing. Listening is a skill which means hearing what the client says and then interpreting what the client actually means. Using active listening skills, such as reiterating back to the client what it appears she has said, can greatly improve the understanding of the client's wishes.
Hands down, composition is the most important skill for a designer to have. Composition is a knowledge-based skill which dictates how an image is arranged. The most important part of composition for a logo designer to know are the Gestalt principles. The Gestalt principles are a set of "rules" that explain how 2-dimensional objects are perceived by the human eye and mind; how a whole may be greater than the sum of its parts. Logos can make use of these principles to create visual interest.