If you can make it by yourself just do it and ask us to review, then we can understand how much you know and what else needed to do in that logo otherwise ask anyone to make a logo for you site.
I changed the look of my site and also made a logo. what do u think? check out the design of the site in my signature
To design the logo one thing should be in you mind that the logo should be meet for you web site concept
Try making a mind-map based upon ideas and attributes that you want your website to put across such as speed and reliability. Then try linking these with simple icons of what you're offering such as a picture frame and attempt to integrate the two together into one icon.
well for designing logo for you website, it should suit to your website theme. So it depends on what kind of website that you have.