Paul, are you a coder, or are you a 'drag-and-dropper'?
And does your site have a simple or a complex structure?
Has it got a graphic design tailored to your current width?
Best bet is to let us have an url to your site, so that we can see what it is like. We might be able to give you some hints, but as Paintbrush says, the topic is simply too comprehensive for this forum..

Thanks for the invite; my website is www.online-superstore.co.uk. I would love to know how do I make this site work just as good as in desktop/laptop PC.

Paul you're going to have to do your homework... Decide whether to go with a separate mobile site or a responsive design.
You could also consider responsive store templates, here's just one example:
http://themeforest.net/item/lexus-mega- … ew/5960349
As is, your site is lacking visual appeal...the flat grey and no products displayed doesn't really say "shop now!".
The fine-print legal disclaimer – the only thing on the home page – isn't much of an enticement to whip out the credit card, either. Look at some e-commerce templates to get some inspiration.

I'm noticing that it's a SCCP site.

FWIW, your site is functional on my iPad.
l did notice a problem with your Google checkout configuration, but l suspect l would have had that same problem using a desktop.

I have found that both ios and Android do a good job rendering any website that complies with WC3 standards. I would start by ensuring that before spending resources on responsive anything.