what type of website? what are your demographics? young people? b2b? old people ;0 ? Is it a blog.... Well you can post up Questions on qna boards asking people if they like the new banner you just created.
Well I run 7 websites that all have the same subject: paid surveys what I have had to do is organic Seo ( search engine optimization ) however this takes a long time but is completely free. You can pay per click to your website however this costs a few dollars per month.
If you really want some help put up your url so we can check out you statistical data and anaylize it.