Do a lot of research into the field you are designing your logo for, look at other logo design from this field and other similar fields to gain inspiration, see what works and what doesn't work so well. What type of fonts are used? Do they work well? What would work better? How is the typography handled? What does the logo design need to convey? What emotive does it need to depict? What is it about the company that stands out that could be represented in the logo design? So on and so forth. You get the idea... Aim to design something specific for the website in question, as opposed to something generic that could be used for any website in any industry.