If you're already on Shopify, just create a new theme within your store and use the Preview feature while you're editing it to see what it looks like. Once it's ready you click publish and now that one is your live theme.
If you're not on Shopify, you can either do a trial, or work with a Shopify Partner/Expert to build on their dev server, then when the site's ready it can be switched live.
My name is Alex, I'm a guru here at Shopify!
No problem at all! You can open a new trial if you wish, but that shouldn't be necessary - you're able to have more than one theme in your shop at a time, and you can work on your new theme without interfering with your current live theme.
When you add a new theme from the theme store, you'll see it appear in your admin at online store > themes below your current theme:
This doesn't affect what your customers see; your current theme will remain in place and prevent any confusion. To work on your new theme, just hit the customize link you see there - this will allow you to tweak that theme and get it looking as you'd like it. Once you're satisfied with the new template, you can go live with the theme by clicking on the actions link and selecting publish, like so:
Hope that's helped! Please feel free to let me know, and you can always give us a call or start a live chat at any time. We're open 24/7 for your convenience and always happy to assist!
Alex | Shopify Guru
the beauty of the platform is that your visitors will continue to see the currently published theme while you're working on the "draft" one.
The switch-over is instant when you Publish new theme and there is no noticeable downtime at all.