How to approach potential customers on facebook?

Thats quite a broad question, can you provide a bit more information? Social media marketing tends to be about building meaningful relationships with customers.

What is the pain your target market experiences that will be solved by the benefit of your product offers that would make it an appealing offer instead of spam?

Do some FB ads and target them and their friends (or influencers/people they seem to respect) with an ad specific to their market segment. Carefully do the following research in creating your ad - Take into consideration their gender, age, are they parents, what they do, where they're from. Do you think they may be influenced by their friends? What other products or groups are they involved with? This might tell you a little more about their personality (fun, lifelong learner, beer enthusiast, etc). All of these little things you can learn about them will help you craft a message (graphics/wording) which may appeal to them.

If you have a good quality product or service that will actually help these people then I would suggest going ahead and joining groups that people are involved with. Start participating in these groups by adding good information to the groups wall, adding articles that would benefit the group, then eventually putting in a little plug for your product. If you do this right you can then Friend people in the group and they will be open to that.

Even better is post articles from other websites about your product / service. Indirectly advertising it by 3rd party reference or testimonial.

Buying ad placement on Facebook is also a great route to go.

If you are looking to join some senior citizen groups so you can push Viagra and Cialis then I'd suggest a different route as that sector is saturated ;)

Few things you can do.

1. Spam, bottom line it works
2. Make sure your fan page is highly customized, You can do the old "become a fan to see a promo code" trick to get more people to become a fan of your page, therefore spreading the word.
3. Facebook Ads, they dont work as well as google ads, but they do work.
4. Give incentives on your site for your existing vistors to interact with your FB page.