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.
Draw up a shortlist of plumbers using a local directory. Online directories will provide you with contact information, reviews and the plumbers' websites, so you can make sure they are suitable.
Some drain leak valves do not take washers and therefore you cannot repair them. If you have a washerless shut-off valve that leaks it will need to be replaced. You will need: a propane torch, solder, flux, sandcloth, a wire fitting brush, a small section of copper pipe (most likely 3/4" I.D.), a slip coupling (again probably 3/4") and a shut-off valve. I would highly recommend installing a ball valve with a drain on it as opposed to a washer style valve. If you purchase a decent quality ball valve it will last a very long time.
Check on the plumber's licensing and insurance. You can ask about this over the phone before you even make an appointment. If the Trustworthy plumber, or his representative on the phone, cannot provide the master plumbing license number quickly and easily, that's your cue to move on.
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.
Punctuality. It is the most important trait of a good plumber. Waiting for a longer time to have your pipes repaired can mean more damage to your property. A plumber who understands clients values time and make it a point to arrive as soon as possible.
In short, the emergency plumber you hire should be from a reputable company. If you think that you can rely on him then you should look for another one. An emergency plumber should be skilled and should be able to deliver quality services to everyone.