Honey bees (Apis Mellifera) range in size from 13–17 mm, depending on gender and maturity. Most honey bees are typically older, sterile, female worker bees that have a furry, brownish-orange thorax and an orange-and-black-striped abdomen.
Honey Bee
Honey Bee at Work
Beekeeper

I am someone who spends an inordinate amount of time, money, and effort keeping honey bees alive, but I understand the danger and inconvenience of your situation. With all of the horrible things happening to global bee populations, anytime someone chooses to eliminate instead of moving a swarm of bees, it is a tragedy. Without the pollinating efforts of honey bees, a lot of the foods we enjoy would not be possible, not to mention we would be missing out on a honey supply. My point is that you shouldn't take killing bees lightly. If you can, contact an apiarist to see if they can remove and hive the bees for you.
First, identify the species of bee. People use the term bee too loosely, in my opinion. You need to know that if the nest is made out of a gray, papery substance, you are dealing with some kind of wasp or hornet. They are even more aggressive, and potentially more dangerous than the most angry guard bee. You need to look at the pictures on this page and do some comparisons online. Bumblebees and carpenter bees are usually plumper, a different color, and have hair in different places. Also, honey bees tend to live up in the air, while other bees live near the ground or in wood holes.
Find a beekeeper. I am a beekeeper, and I think it's important for you to know that this is the perspective from which I am writing this article. As a beekeeper who spends $70–$100 for a couple of pounds of bees and a queen for each new hive I tend, I can tell you that I would welcome the opportunity to rescue a swarm and put it in one of my hives. It is important to note that not all swarms are created equal: if it is a free-formed ball of bees hanging from a tree branch or a fence post, I can deal with that in a minute or two; an established hive is far more difficult to handle.
Remove things that attract bees. If you notice an increase in activity, or if you find you've been getting stung more often, it doesn't mean that there is necessarily a hive of bees nearby. Bees can and will fly several miles in search of food. If you have a good source of food in your backyard, you could just be attracting a lot of attention. If you have a lot of flowering plants or fruit trees, you shouldn't be upset about having bees buzzing around, as those bees are going to improve your harvest! If you have a dumpster which is full of sweet, syrupy garbage, or a hummingbird feeder, bees are probably going to appear there, as well.
Finding a beehive will require some observational skills. I recently found a nest of feral bees, 20 feet up, in a partially dead box elder tree on my property. Most people probably wouldn't have noticed it, but I spend a lot of time looking upwards at birds, which is how I noticed a cloud of activity on a warm, summer day. I decided to leave them there, as I figured they weren't hurting anybody. Finding your nest of bees is going to require that you do something similar, whether it be in a tree, barn, garage, or the wall of your child's playhouse. Look for bees congregating around the hive entrance, especially on warmer days.
Make plans, bee prepared. Is the hive up in a tree? Is it inside of a building? Is it inside of a wall? All of these scenarios require a different set of tools. The first thing you always need to think about is your safety and the safety of anyone who might be in the general vicinity of your bee removal operation. I suggest either buying a bee suit, or fashioning one out of heavy-duty coveralls and mosquito netting or window screen. The important thing is to tape up any openings and keep the screen off the skin a bit, or they will find a way to sting you. A tool like a hive smoker can be useful for calming the bees, as well.
Relocating bees would be the best thing to do. This is easier when the swarm is new and hanging in a clump somewhere. Basically, you just need to cut the branch or thump them into a box. If the queen goes into the box, the swarm will follow her. I would then relocate the whole bunch into a tall hive, brood super box with 10 foundation frames. If the bees are established inside of a building or inside of a wall, salvaging the colony is extremely difficult. Any attempts at removing material will excite the bees, and you could lose or kill your queen in the process.
It's not hard to kill bees; just point and shoot. If it is not possible to relocate the swarm, or if the colony has established itself in a place that makes it impossible, killing the bees might be the easiest and safest thing to do. Attack the nest in evening hours, when the bees are the least active and in the nest. If the hive is exposed, the projectile, wasp nest aerosol spray will work well. If the hive is within a wall, you will want a dust-based insecticide, which you can puff into entrance holes of the hive. Check back the next day for more activity, and treat again if necessary. Be sure to remove dead bees and hive material from your walls.
If you haven't been able to find a willing apiarist, and you don't feel comfortable taking on a nest of bees by yourself, then the safest and smartest course of action you can take is to call an exterminator. Bee stings are nothing to joke about, and you are risking your safety and the safety of others the longer you put it off. It shouldn't be too hard to find an exterminator with a quick Internet search or a glance at your local yellow pages. A professional will have the protective equipment necessary, and a wide selection of chemicals at their disposal. Yes, it's sad that some bees have to be killed like this, but there is nothing we can do about it. If you have an interest in keeping bees, I encourage you to join a beekeeping club and find out if your local college extension offers beekeeping classes. It's a great hobby that promotes a healthy planet, raises awareness, and increases bee populations in a safe way.

Flight paths. One nonfatal honey bee control method involves adjusting the bee's natural flight path using fences and borders. Most run-ins I've had with my bees have been my stepping into an obvious flight lane between the hive and a food source. If you live near a kept hive, ask the apiarist to add taller fences around the area. This forces the bees to fly higher, thereby making it less likely for our two heads to meet.

Smoke. When handling bees, I always use a bellowed hive smoker. Most people think that the smoke has some kind of chemical calming effect on the bees, but according to my beekeeping teachers, this isn't true. It's actually an instinctual response to retreat back into the hive at the smell of smoke, making them easier to handle.

Bee stings. If you should find yourself stung by a bee, first remove yourself from danger. Search for the stinger. If it is still in your skin, wipe it away quickly. Apply ice and an antihistamine cream. The pain should subside in 90 minutes or so. If you feel itchy, start swelling up, or feel a shortness of breath, you might be allergic. Use an EpiPen, if you have one. Otherwise, get to the emergency room immediately.