Please note that the following opinions are my own and do not necessarily reflect the views of my employer.
Figure out your branding
I can’t tell you how much easier it is to design a website when provided with catalogues, past advertising campaigns, copy that is indicative of your company’s voice, etc. When you know where you’re going, it’s much easier to follow you there. Occasionally, I’ll be given a “go nuts with it” or “we’ll provide the logo later” spec, but chances are good that I’ll go in a completely different direction than you were envisioning. If there’s a disconnect between your designer and your brand image, your website will stick out like a sore thumb.
Done poorly

In my opinion, the Laura Ashley redesign is a great example of what happens when the designer doesn’t fully understand your brand image. If you have a look at their catalogue, Laura Ashley is all about texture, traditional British patterns with a touch of shabby chic. The website now looks too “John Lewis” and not enough “Cath Kidston.”
Other branding confused sites are Ted Baker, The White Company (post-redesign), and Gucci. I won’t expand on these, but feel free to ask me about them in the comments if you’re interested.
Done well

Kate Spade is one of my absolute favourite online stores right now. Not only do they have a “Play” catalogue section that they keep updated, but the colours of the entire site change seasonally to relate to the product line. The website screams “utility, wit and playful sophistication” which is coincidentally how they describe themselves on the about page.
Other noteworthy sites that relay the brand well are Joules, Hollister Co., and Habitat.
Get your photography done first

This kind of goes hand in hand with branding. You can ramble off the usual adjectives (clean, simple, organized) to your designer, but if you show your product lifestyle photos and/or some creative photos of your shop interior, we will be way more likely to get the design right the first time. Plus, isn’t it so much nicer to look at a design mockup with your lovely images in place?
A lot of the time, clients will have us whip in some stock images while they get their photography together. This works, but hunting down appropriate stock images is not really great use of my time. I’d rather be laying nice typography over your actual lifestyle images!
The entire web design can hinge on the photography; this is especially true of fashion stores. How boring would the Reiss layout look with grey boxes in place of the photos?!

Bornshoes.com is another excellent example. The lifestyle shots define the brand, own the layout and make this website. The photography in the background scales with the window, too (which is kind of hard to illustrate from this little thumbnail so go and have a play with it). If you’re interested, they also have a behind-the-scenes page about the photography team.

Know your competition
What is your competition doing well? What could be improved upon? What will drive users to your store, as opposed to theirs? Does your product have a specific feature that theirs doesn’t?
Our most successful clients have done this well. Sometimes it can be as simple as an uncluttered design or approaching the main navigation differently, but other times clients have had to offer additional services or add extra functionality (such as interactive catalogues or liquid layouts) to their site.
Inject personality
Does your brand have a unique voice? A character, perhaps? An interesting and relatable personality is far more likely to get sales. Same old, same old is boring! Be brave!
An obvious way of injecting personality is through a blog. Any lifestyle store should definitely have a blog accompanying it. A blog will also help with your SEO and returning visitors as well as refer readers to relevant products. I think that Lilly Allen’s Lucy in Disguise store website leaves much to be desired, but the blog posts written by fictional character Lucy are interesting, unique, and enough to persuade me to keep visiting the site.
Done well

Marie Catrib’s is just so dang adorable. The personal touches and handwritten copy draw you in.
Don’t be too vague or too specific when briefing your designer
When it comes to explaining what you like and what you don’t like, keep in mind that you’ve hired a professional for that very reason: they are a professional. Don’t stifle their creativity.
Try not to limit yourself to one inspiration website (cough, John Lewis, cough) but be careful not to provide too many.
In fact, these days I actually prefer to work from a list of adjectives and lifestyle photos, when possible. Inspiration websites are fine and I do like to discuss which sites you like and why, but the why is the important bit. There’s nothing more confusing than receiving a long list of websites with contradicting styles and not knowing how to interpret them. You need to say what you like and why.
Equally important when briefing your designer are sites and styles you do not like. I find this probably more useful than just hearing about sites you do like. No left navigation? No problem. No dark backgrounds? Cinch.
What style do you like? Grunge? Clean? Collage? Grid-focused? What layout style suits your brand and why? Figure out what you’re after and make us designers understand you, but give us room for creativity. If we’re meeting face to face, I actually like to scribble up layout wireframe ideas right then and there. I think most designers will probably happily do this with you. It’s good to start off the project on the same page.
Know your statistics
What’s your conversion rate? What age range are your current shoppers? Are you looking to expand your target market? How will you market to them? What browsers do current shoppers use? Do they abandon their carts? Are they likely to become loyal customers?
Knowing a lot about who your customers are and how they shop will help you immensely in redesigning your store. Adding loyalty cards, referral campaigns, recommendations, etc are all do-able, but are they worth their while?
Be social
Build up your fan base by being active on Twitter & Facebook. An easy trick would be to hold contests & giveaways, tweet about them with links shoot potential customers off to your blog. Offer exclusive discounts through your email newsletters and tweet like crazy about this. Create conversations by asking questions with the new Facebook Questions feature.
Stay relevant and tech-savvy by any means necessary, and use your brand’s developed personality to really sell it. It really depends on your product, but you could send SWAG to YouTube weblebrities or relevant bloggers in hopes that they will promote you. (Hint, hint!)
Hopefully this is helpful. There’s probably a lot that developers could add to this; feel free to comment below!