Fishless cycle:
Fill your new tank with water, treated exactly as you would treat it for fish - dechlorinate, etc. Make sure the pH and all parameters are where you want them. Start the filter up - complete with all filter media, cartridges, etc. Add the gravel or decorations or anything you plan on using, except perhaps plastic or real plants. Add a heater. Bring the water temperature to 78-80 degree F.
Add pure ammonia. You can find pure ammonia very cheaply in places like a grocery store, nnnnnn, etc. Do not use sudsing ammonia - if you shake it it will foam - for this has added soap. I cannot tell you exactly how much ammonia to put in, for each ammonia is a different concentration, but put in 1-2 ccs and test the water. What you are trying to reach is a level of 2-3 ppm ammonia. This would be toxic to fish, but, since you have no fish, it is ideal. (If you go over, that is ok. Try not to go past 4-5ppm, though!

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Now, the hardest part comes. Do nothing. Do not add anything. Do not change anything. In a week or so, test for ammonia and nitrites. If your ammonia levels have dropped and nitrites have started to emerge, you know you are on the way. You can add a drop or two more of ammonia as needed to keep the ammonia level at about 2ppm.
The nitrogen cycle is: Bacteria process ammonia into nitrite. Different bacteria process nitrite into nitrate. You change the water and rid it of nitrate.
The first type of bacteria usually grow rather readily and are soon processing the ammonia into nitrite. Your nitrite levels will rise. Your ammonia levels will drop. The second type of bacteria that process the nitrites into nitrates are a little more touchy. They take a bit longer to get going. Once you are reading nitrites you can begin to test every day or two for nitrates. Your nitrites will spike very high long before you see the nitrates appear, most likely. When you see nitrates beginning to appear, you know that your tank is close to being cycled.
AS the first type of bacteria process the ammonia into nitrites, the ammonia levels will, of course, drop. But since you need to keep feeding these bacteria, you need to keep adding a small amount of ammonia every day or so. A 1/2 cc or so should keep the level at about 1 ppm for you. Test to make sure. Before long, you will find that the tank has zero ammonia and 5 nitrites and zero nitrates. Add a little ammonia to 1ppm. Then it will be zero ammonia, 2 nitrites, and 5 nitrates. Add a little ammonia. Then it will be zero ammonia, zero nitrites, and 160 nitrates.
At the end, if you can add ammonia in the morning to 1ppm and have it reach zero and the nitrite reach zero by the next morning, your tank is cycled. It is now time to do a large water change. Start with a 50% one. Test the nitrates. If they are not below 20ppm, change some more water. When the nitrates are below 20, the nitrites and ammonia are zero, you can add fish.
It is ideal that you are only adding the one fish. His waste will start to feed the bacteria colonies. You may get a bloom of bacteria when you first add the fish. This is the colony of bacteria responding to the new food - the more food, the more the bacteria reproduce and the extras can float around in the water giving it a whitish haze. This is normal and should clear in a few days. You should test the water of a newly cycled tank every day for a few days to make sure that the cycle is holding.
Fishless cycling is the easiest, for you have no daily water changes and no worries about your fish dying or being injured by poor water quality. Congratulations on deciding to use this wonderful way to get your tank going!
If you have questions, please ask! The hardest part of all is waiting - it can take a couple of weeks - sometimes only a few - sometimes longer......