Yikes! You should know who your customers are BEFORE (and as) you develop your product, not after.
I would assume you first might create a product for a specific type of customer.
But if you are starting a product, here is an idea using social media:
1) Open a twitter account
2) Do some searches on keywords related to your product. Find which ones have more recent tweets. (If you see 5 tweets in the past 5 minutes, that is more popular than one for example you see 5 Tweets in the past 5 days)
3) Post some tweets. Offer some advice or ask questions relating to your product area. Make sure you add some popular keywords in your tweet.
4) Retweet (or reply) to other tweets from your search results. Offer advice, opinions.
5) Add people with similar interests to your product area. (Found doing searches)
6) Using the above find people and ask if they want to take a short survey relating to your product area. Find and even ask some people if they want to do some alpha testing of your product.
Just one way to start up an online discussion and start a process to discover new customers.
To start, I'd hope you developed your product for a specific problem that a group of potential customers may have. If not, it might be pretty hard to find those customers.
In saying that, if you have an alpha, you may not be too far down a specific track. Get your service out there, and ask the people using it what they need it to do - ask the right questions and they will design the product for you. Then you just need to build it!
Great products are a way to solve someones pain. It hurts them that they cannot do what they want in a particular way, and the product lets them do it faster/cheaper/better/in a whole new way. This is why the customer is willing to pay money for it. They work hard for their money, and want value out of the things they spend it on.
In general, knowing who your potential customers are is something to think about before you start working on your alpha version. If the product is something you created for your own pleasure then its fine, because your are probably your own first customer.
Assuming that your product brings value and prevents someones pain, its simply a question of who is in pain, and how do you reach that audience. Think about all the "players" involved in using the product... By that I mean for example if its a toy for children, then you need to think about the kids and their friends, about the parents, about their teachers and the store owners. To each you might provide a different value, and each might be your costumer. If you were dealing with technology for a house, think about the tenants, building managers, architects, developers, real estate investors, mortgage banks and the stores where the product might be sold. If your product is a web 2.0 service, start twittering about it, try to get as much hype as you can, and your potential customers will figure out what to do with it themselves :)
While there are probably some uses for you product that you will never think of by yourself, these are not the initial ones you should be focused on. Once the product is ready, feel free to put it online, and your potential customers will start finding you (after some SEO work of course).
Sounds like what you're asking may be "I have this product, and some users who are testing it. I want to know if there are any real groups / segments within my user base that I could target and focus on as I develop my product".
This is a normal question when you're still working out the real value proposition and format of your product. The way to deal with it (from a product management point of view)is to ask any customers you already have. (I'm assuming here that you have a software/web based product and can easily reach out to your current users.)
I would do this in 2 simple steps:
First, contact 10-20 people directly - invite them to a chat room, email them, whatever. Have an open ended conversation, and get an idea of why they are using the product / what they get out of it. You'll be surprised by what you hear and learn from just such a simple exercise.
Second, tally up the different uses / kinds of users for your product, and do an actual survey of all of your users. A simple multiple choice/other kind of question format will help you get an idea of how big each group is. That'll get you started focusing on the actual customers, and may give you good ideas for new products/features/customers whom you hadn't known about before.