Ask around. Ask your friends, ask your neighbors and get referrals. Nothing is more powerful than the testament of someone who has had a local plumber in their home and can speak to his/her capabilities.
Do independent research using the Yellow pages, search engines and local business listings. Beforehand, make a list of what you are seeking in a plumber on Long Island. For example, years of experience, what services they provide, whether or not they have emergency service, areas of expertise, types of jobs they perform (residential, commercial, industrial) etc. Look for local plumbing service companies that are a match.
After you have used this method to get a feel for the three or four best plumbers that seem the most reliable, it is time to start making phone calls and sending emails. Be specific about exactly what you want done and ask for quotes. Be very careful if you get offered a seriously low quote. If something sounds way to good to be true, it probably is not. Do not be scared of asking questions. Remember you are in the driving seat these faucet replace people need your business. Ask for testimonials from their previous customers. Make sure that they are properly trained, ask what certificates they hold and whether their work is fully insured and guaranteed.
For instance if you are looking for a Trustworthy plumber, you can post a tweet in Twitter and ask for referrals. Be careful of spammers who may connect with your keywords. Trust the comments that come from within your network.
The number one thing to look for is emergency services. You never know when a pipe will burst or a toilet will overflow. It is not always during business hours, and you certainly cannot wait hours until a Local plumber is ready to come to your home in the morning. You need someone who will be responsive when you need fast help, which is why you should look for a company that provides emergency hours. You may have to pay an extra fee, but it is usually cheaper than having to pay for mold elimination down the road after letting standing water stay in your house for days.
Here's an example. Let's say you are a plumber. Will people put "plumber" into Google to try to find you? How about "plumbers"? How about "plumbing"? All of these are valid search terms, but they each reflect a different "conversation" in the mind of the searcher.
Once the work has been completed, ask for a breakdown of the bill before it's paid. That way, you know what you're paying for and it stops the plumbers asking for more money down the line.