How can I grow my new business?

Hmmm...with all this information you provided, I am sure you will get some very insightful answers to help you out.

Ok, I'll bite....Advertise?

Best way to advertise my business?

I would really think that with the first line of my comment to you that you might have got what I was trying to say...

Ok, I will spell it out for you:
You gave us absolutely NO detail as to what your business is, where it is, what you sell or do, how long you have been operating...nothing....yet you think we can just magically tell you how to grow the business.

So now you want to know how to advertise....AGAIN....What is your business? What do you sell or do? Where are you? How long have you been operating? Have you tried anything else?

You can check out my website for my business Flower Delivery.

The site is confusing. I don't see any flowers or gifts, only cakes. There's no information about delivery. There's no company information. The "menu" is very inadequate. I don't know how much the products cost or what the delivery charges would be. Why would anyone want to order -- there's no "hype" or testimonials about your products and services.

In other words, even after looking at your site, I know nothing more about you and this business.

WG is right. Your website doesn't really sell the product if you understand what I am saying.

Aside from that, now I see that you are trying to sell through a site....this is harder to do. I have a T Shirt sales site and it's tough because you have to get search engines to recognize you. I have advertised on Facebook and Twitter as well as using Google Adwords. Fix your website, make it sell the product...make it clear what you've got and why people want to buy it from you....then work on getting people to see it.

No offence, no one would know that website was basically created to sell cakes or flour or any product whatsoever without you having to say so.
However having a professionally designed website isn't a guarantee that your sales will improve if your local environment (which I believe is your target; due to the nature of you product) lacks the "internet culture".
If you really want to grow your business, you must first define your target customers, understand them, understand their buying culture and then tailor your marketing strategies to their culture.
The key to growing a new business whether big or small is marketing. Always remember that.

First, cacman, he needs to have a strong and interesting web site with useful, desired products before he can market anything.

Having an interesting website is a marketing strategy but isn't the only one available. What if he lives in an area where the internet is not very popular? What if people in his area don't know much about online trading?
In most part of Africa for instance, the internet and online trading in particular is far less than what it is in Europe and America.
In America for instance one can buy virtually all he wants from the comfort of his living room by just clicking a button or two.
That scenerio isn't obtainable everywhere that's why I advised he should understand his target. If his target comprises mainly the internet savvy kind, then a good website will obviously be a key strategy otherwise, he should choose a strategy that will be more effective bearing in mind that his supplies cannot go beyound a certain boundary due to the nature of his product and the current state of his business.

Do you have a bricks-and-mortar business and this would be an add-on plus another way to find customers?