My good friend and colleague Dave Jacobsen recently posted a great article on LinkedIn about logo design. It's something that most designers have to do fairly often, usually for a client who's never had it done before. The first step is almost always to educate the client to some degree about logo design - sometimes to the extent of clarifying what a logo is, but usually more on the order of explaining what makes an effective logo. This article by Pamela Wilson at bigbrandsystem.com provides the best summary I have ever seen: "look for a timeless, original image that’s simple, and can be reduced to black and white and used very small."
When I create a logo concept for a client, I always begin with a design in solid black, because if a logo doesn't look good in solid black, it's not a good logo. The finished product, apart from exceptional cases, should use no more than two colors other than black - with a solid black version provided, and possibly also a greyscale version. A good logo should always be designed in vector format and then exported into non-vector versions as needed, never the other way around.
I've had people provide me with logos that they or someone else created (invariably in Photoshop) with way too many colors, and often with gradients, bevels, "glows" and drop shadows that a good design doesn't need. I then have to explain to them why it will be impossible,or prohibitively expensive, to print or reproduce. I've worked with people who want me to adapt someone else's logo with their name, and then have to explain why that's a bad idea.
Logo design doesn't have to be difficult or frustrating if you start at the right end of the process, and (may I humbly recommend) engage the services of a professional.