There is only one real way to know - let them tell you. You have to start somewhere with a new website design so if you have a good eye for design and know who your customers are then make your best effort with a design of your own.  Most often though it is helpful to have an objective third party (like me) commenting on what you need to get started.  After that you need to start asking the visitors.  So, how do we do that?

By testing and by asking.  The easy solution is to create a feedback poll, forum, or other feature inviting visitors to share their impressions.  This can get burdensome in hurry.  The most often used tool is testing.  Testing typically involves making one change and then measuring the results.  This is most effective when you have significant traffic on the site.  If your traffic volume is low then you will want to ask because that will get you answers more quickly.

Here are some starting points for new websites.

• Consider a template. Depending on the technology you are using for our website there often are numerous templates available at a reasonable cost.  Templates are often much less expensive than a custom graphic design.
• Consider your competition. Visit websites of your competitors as well as sites for different businesses or industries that sell in a similar way or accomplish similar objectives.  You want to make sure you differentiate yourself from your competition.
• Consider your resources.  How much time can you spend on your website design?  How long will you be able to use this design before you want to or need to change?

I have significant experience with owners of new websites.  Most are intent on optimizing their website design from day one.  And, significant time is often spent on the design.  Sometimes more than on the content.  But, my experience tells me that typically within the first six months (could be three months to a year) these new website owners want to change the entire design of their website.  Some just don't like it any more.  Some realize that customers don't like their initial design.  Some realize that their initial design doesn't support their content.  Some realize that they just didn't really know what they wanted the website to do for them and when enlightenment sets in they know they have to change.

They don't build cars with just the body in mind.  It needs an engine sufficient to get you going when and where you want.  It needs lots of parts and systems that are integrated and work together smoothly.  And, just like any car your website is going to need maintenance.  So keep the maintenance in mind as you start so it will be easier later to make your website better.