If you're not using their templates or their software, then you would have to learn website coding and/or get some software yourself
(such as dreamweaver or golive), which could be costly, if you're doing it all yourself. If you have something specific in your head, you could describe it in detail to a web designer (we do this, in case you're interested: www.leppdesign.com), then they could actually build it with code for you.

Some hosting companies do offer eccommerce software, but depending on the kind they've chosen to offer, you could be limited on the design of it.