This instructable features honey harvest and extraction. While it is less likely that anyone would do this on their own if they are not a beekeeper, this might be useful for those who aspire to become one.
Bees are really great and easy to keep, even in the urban environment! As Novella Carpenter calls them, bees are "gateway animal for urban farmers". All you need is some space in the backyard/deck.
The process of honey harvesting and extraction most likely happens on a separate days. These are the tools required:

Honey Harvest
1) beekeepers suite - mesh helmet and folding veil would do it, with some layers of clothes
2) smoker with fuel (dry branches, leaves, etc.) and a lighter
3) frame super - where frames with honey combs will be put for transportation
4) sting resistant gloves
5) hive tool - to move the frames, scrape wax, etc.

Honey Extraction
1) heated knife - to unseal honey cells
2) uncapping fork - to unseal honey cells missed by the heated knife
3) tub for wax/honey
4) extractor! - fancy cylindrical piece of equipment, used to extract honey
5) food-grade bucket - to catch honey out of the extractor
6) double sieve - catches wax and impurities as honey is poured from extractor
7) containers - final destination of honey before consumption

Step 1: Introductions

Before we begin, let me first introduce Her Majesty: Apis mellifica (honey bee in Latin)! Also, here are some hard working worker bees, bees with pollen on their legs and one cutie stuck in the nectar with pollen! They collectively make a honey harvest possible!

Step 2: Part One: Harvest

Light the smoker. Use dry branches, hay or newspaper. The smoke dulls the bees' receptors, and prevents them from releasing the alarm odor, a volatile pheromone. The smoke also makes bees gorge on honey, which further pacifies them! Just think about it: how mad would you be if someone got into your house and stole your preciousness?!

Step 3: Prepare Supers

The frames with honey comb are transported in supers. Have them handy. You may also want to have a cloth to cover the super with frames full of honey to prevent bees or other insects from getting to them.

Step 4: Open Sesame

Using the hive tool, lift the hive lid and blow some smoke in the hive. Open lid slowly. Our bees were pretty calm, but that is not always the case!

Step 5: Honey Frame Inspection

Pull the frames out of the super and inspect the honey combs. Depending on how busy the bees were, how warm it was and if the hive didn't swarm, you may have anywhere between 20 to 100 pounds of honey!

Inspect frames. Uncapped cells with some nectar in it are not harvested; only sealed frames are.

Step 6: Inspect All Supers

Depending on the hive configuration, there might be multiple supers to inspect. Take the super off the hive and move it to a clean surface. Repeat.

Step 7: Scrape Extras

If there are any extra cells in between the supers and frames, scrape it off with a hive tool. Make sure to taste it right there - there is nothing like nectar, honey and wax freshly harvested!

Step 8: Let's Harvest Some Honey!

Pull out the frames with honey and put them in the harvest super. All the cells should be sealed. Each frame can hold on average 6.5 lbs of honey, so it may be heavy!

Step 9: Honey, Brood, Nectar or Pollen?

The frames may have different colors of honey combs. The light one is pure honey. The darker one has pollen. The capped brood (the final stage of development for a bee) is tan in color and located in the center of the hive.

In the pictures below, the crescent shape of the combs indicates where a brood was before; it now is packed with pollen and honey. You can see the nectar shine at you from the open/uncapped cells.

Step 10: How Many Are They?

How many bees per hive on average? 50,000! That's a lot of bees!

Step 11: Part Two: Extraction

Now the best part! Take the frame of capped honey. Mount the frame above the tub for wax and honey. Use the heated knife to unseal the cells. Lean the heated knife on the edges of the frame and under 30 degree angle and move "fast" - don't linger too long, it burns the honey! Repeat for both sides of the frame.

The heated knife takes off most of the caps. For the leftover ones, use the uncapping fork and gently shave off the caps.

Step 12: Let 'em Spin!

Preheat the extractor. Place the uncapped frames in the extractor, as you uncap them. Once all the frames are secured, close the lid and start the extractor. It should start slowly, then speed it up. Within 10-15 minutes, all the honey will be out of the honeycomb, stuck to the bottom and sides of the extractor!

Step 13: Pour Out Slowly!

Place your food-grade bucket under the extractor spigot. Use a double sieve to catch the wax and impurities as the honey starts pouring out of the extractor. Do not leave the spigot unattended - you will be surprised how much honey comes out!