Is there any website which can help me in designing an e-commerce website?

Go with GoDaddy ...

It has a user friendly website builder and its very cheap ... I recommend it for non-techies.

Please can you elaborate more; do you want to start an e-commerce website for your self or you want to design it for a client of yours?

Anyway I prefer to use an e-commerce platform such as BigCommerce they are well known and trusted also you can choose form their own templates and easily you can change the design depending on your needs and tast

Good Luck 

If you need any help .. i will help you for free :) .. 

check deviantart.com to be inspired with drawing the theme and check themeforest.net to get a general idea.

it you want to a eCommerce website i personally recommend you for Shopify.com  it is nice and you can get you website in3 minutes only

there are everything available on this site E commerce website theme, Payment option etc.

to learn how to make a e-commerce website it's not a problem at all there is so many videos and websites which contains topics on that like

https://www.youtube.com/user/qatarit

https://www.youtube.com/channel/UCzEYvv6Ciw_fnRIqK0cFdRQ

http://worlddes.com/vb/

http://www.tahaworld.com/courses/course/38#.VOebbfmUeI8 

 I recommend going with hosted versions  Magento E-Commerce 

Shopify can be a good choice if you want to handle everything yourself, they offer templates plus payment gateway as well. 

but if you require your own custom website then WordPress with WooCommerce can be your best choice for small eCommerce sites.

But if you are thinking to launch a major product catalog website then you need to hire a web developer who can deep-code Magneto... 

I recommend http://www.shopify.com/ . They are professional and they offer different packets. 

Start Your e-Business. Many Opportunities under one roof. 

Middle East web projects :)