This is the method I have used to cycle 5 tanks (from 2.5 to 75 gallon) and it has worked perfectly. I think it is the simplest and requires the least amount of work. First add your ammonia to raise the level to 5 to 6 ppm. Now you simply wait on the ammonia to drop back to around 1 ppm. Spend the time researching the fish you like and see if they are compatible with each other, with your tap pH, tank size, etc.
Test daily to see what the ammonia reading is. There is no use to test for anything else. Nitrite and nitrate won't be present until some ammonia has processed. Ammonia will raise your pH so no use to test it either. Once you see a drop in the ammonia, test for nitrite. There should be some present. When the ammonia drops back to about near zero (usually takes about a week), add enough to raise it back to about 3 to 4 ppm and begin testing the nitrite daily.
Every time the ammonia drops back to zero, raise it back up to 3 to 4 ppm and continue to check nitrites. The nitrite reading will go off the chart. NOTE FOR API TEST KIT USERS: When you add the drops, if they immediately turn purple in the bottom of the tube, your nitrites are off the chart high. You do not need to shake the tube and wait 5 minutes. If you do, the color will turn green as the nitrites are so high that there isn't a color to measure them with. Once the ammonia is dropping from around 4 ppm back to zero in 12 hours or less you have sufficient bacteria to handle the ammonia your fish load produces. Continue to add ammonia daily as you must feed the bacteria that have formed or they will begin to die off.
The nitrite spike will generally take about twice as long to drop to zero as did the ammonia spike. The reason for this is two-fold. First, the nitrite processing bacteria just develop slower than those that process ammonia. Second, you are adding more nitrite daily (every time you add ammonia, it is transformed into nitrite raising the level a little more) as opposed to the ammonia, which you only add once at the start and then waited on it to drop to zero. During this time, you should occasionally test for nitrate too. The presence of nitrate means that nitrite is being processed, completing the nitrogen cycle. The nitrate level will also go off the chart but you will take care of that with a large water change later. It will seem like forever before the nitrite finally falls back to zero but eventually, almost overnight, it will drop and you can celebrate. You are almost there. Once the bacteria are able to process 4 or 5 ppm of ammonia back to zero ammonia and nitrite in about 10 to 12 hours. You are officially cycled.
At this point, your tank will probably look terrible with brown algae everywhere and probably cloudy water. As I mentioned, the nitrate reading will also be off the chart. Nitrates can only be removed with water changes. Do a large water change, 75 to 90 percent, turn the heat down to the level the fish you have decided on will need, and you are ready to add your fish. You can safely add your full fish load as your tank will have enough bacteria built up to handle any waste they can produce
