fishless cycling
Conventional cycling involves the use of hardy, "starter" fish. While these fish are able to recover from the stresses of cycling, they undergo considerable suffering while the process is underway. There has been some discussion that the tissue damage is so extensive as to impact them permanently - reducing their lifespan.
Fishless cycling is a method by which cycling-like conditions are created in a tank without actual fish being present in it. That causes ammonia-eating and nitrite-eating bacteria to begin to grow and spread and create a tank that is ready and cycled after 4-8 weeks for live fish to be placed there.
Key to the process is creating a tank environment which simulates fishes eating and pooping, i.e. an environment in which ammonia is steadily being introduced into the water and can act as food to enable the everpresent ammonia-eaters (aka Nitrosomonas) to begin growing to beneficial numbers. Since we're going to create and track a specific chemical environment in the tank, it is important to have the three key tests (Ammonia, Nitrite, Nitrate - $8 each if you buy the Aquarium Pharmaceutical brand from your local fishstore).
The process
- Step One - Seed the tank with bacteria from an established tank - that usually speeds cycling considerably. How can do you this? Buy or borrow gravel from a known established tank (many fishstores will happily sell it too you - gravel is the cheapest thing in the world). Or borrow some other thing that bacteria could be growing on from an established tank (the porus filter material is great). Take care to scan the tank and tankmates for any sign of disease. You don't want to seed your tank with an epidemic.
- Step Two - Begin a daily regimen of adding Ammonia (or something that will generate Ammonia) to the tank.
- Step Three - Monitor Ammonia, Nitrite and Nitrate levels in the tank daily. Watch the Ammonia rise to between 3ppm and 5ppm, and then keep it there. If it goes above 5ppm, do 25% water changes (every 4 hours if necessary) until it comes down to 5ppm. Continue adding your daily Ammonia or Ammonia-source though, don't stop.
- Step Four - Watch as Nitrite comes into existence and then climb. This means that the Ammonia-eating bacteria are getting established. They are consuming the Ammonia and excreting Nitrites. Let Nitrites climb to 3ppm, but no further. If they exceed that, do 25% water changes to bring them back down below 3ppm.
- Step Five - Watch as Nitrate comes into existence and it climbs. Now the Nitrite-eaters are getting established. This is a more temperamental bacteria than the Ammonia-eaters and can sometimes take their sweet time. Don't allow Nitrates to cross 30ppm - do water changes if they do (you can get algae growth above this).
- Step Six - Watch as Ammonia drops to zero, followed by Nitrites falling to zero. Confirm this across a couple of days.
- Step "Get the fish" - Your tank is ready. Bring on the fish, and stop adding the daily Ammonia (or Ammonia-source). Remember: never add more than 2 fish per week. Monitor Ammonia, Nitrite and Nitrates as you were before. You can get a mini-cycle happen anytime you add new fish, but it is tiny compared to the initial cycle and most fish deal with it just fine. If Ammonia or Nitrite go to or above 0.5ppm for more than 2 days in a row, do 15-20% daily water changes until they subside back to zero.
Where would we get ammonia from? Flakes is a good answer
It turns out that rotting food creates ammonia. So, you can add flakes to the tank, as though there were fish there. Don't add too many - just a pinch a day, say 4 large flakes for a 10 gallon tank. As the flakes decompose, they will create Ammonia. Since food has other stuff in it (such as Phosphates) which can be harmful in big concentrations, remember to do water changes before you put any fish in. The decomposing flakes will also leave debris, which you should suck out (with an aquarium vacuum) as best as you can before you put fish in. Also, the exact concentration of Ammonia is not directly controllable with flakes. It depends on their type, amount and speed of decay. There will be a time lapse before Ammonia begins to build-up, and some erratic behavior to Ammonia levels even after it does, which will cause cycling to take longer than you want. But this is a legitimate way to cycle your tank.
Real, measurable Ammonia is the perfect answer
Ammonia is used for cleaning (in the Ammonium Hydroxide form where it is combined with water). 
That Ammonia can be used very effectively to cycle a tank, with one important caveat. Cleaning (or Janitorial) Ammonia often comes mixed with detergents or fragrance. Both are toxic to fish, and detergents will kill them swiftly. Unfortunately, Ammonia with detergent is almost never labeled that way. A strong indicator of detergents is foaming when you shake the bottle. Pure Ammonia does not foam. One good, known detergent-free brand is Ace Ammonia (Janitor Strength, 10% Ammonium Hydroxide, $6).
Once you have the ammonia source you need, the first thing to do is figure out how many drops it takes for you to get to 5ppm for your tank. Take one gallon of water in a bucket and add the conditioner you normally would. Now add Ammonia until you reach between 4-5ppm as measured by your Ammonia test. Take the number of drops you needed and multiply by the capacity (i.e. number of gallons) in your tank. Add those many drops of Ammonia to your tank. By this simple step, you will have instantly reached levels of Ammonia that flakes or fish would have taken at least two weeks to get to.
Now all you have to do is keep "topping-off" daily with additional Ammonia over the next few days so you stay at the spike levels (4-5ppm) - some hit-and-miss is acceptable. Count the approximate number of drops this takes, and from then on add that number daily (i.e. stop trying to make Ammonia spike anymore - just focus on the number of drops). As with the flakes, wait for the nitrite spike and then for both ammonia and nitrites to fall to zero. At this point your tank is cycled, and there will be nitrates in the tank. Start doing 20% water changes every 6 hours to get nitrates below 20ppm, and add fish.