How Can I Speed Up The Cycling Process?

  You can find someone with a healthy well established aquarium who will give/lend you some gravel, plants/decorations, and filter media to seed the beneficial bacteria a cycle cultivates.

If that's not an option, cycle without fish. This is the fastest and most humane method.
Seed the tank with filter media or gravel from an established tank, that brings in some real live filter bacteria that can them multiply and colonise the rest of the tank/filter. Squeezing a dirty filter into the new tank, or even gunge syphoned from a running tank will all act as seed material also.



Increase the temperature, take it up to about 85F. The bacteria will multiply faster in the warm water.



Add live plants, they form part of the cycle anyway, and probably have cycle bacteria on them as well.



If you add enough working filter media and/or plants it's actually possible to instantly cycle a tank, at least to a level where it's safe for a small number of fish.


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Ian
I've got 5 fully cycled tanks that all started with a bag of mucky water from an older tank. Obviousy make sure the old tank is healthy and I just dig the siphon into all the crap between the gravel, suck it all up and put in the new tank. Sounds disgusting but I've never had a problem with cycling.
Well if you have gravel that is clean and used previusly that can make it go faster. If just starting you can't do much you can do
Using filter media and gravel from an established aquarium is the only way to speed the process up safely.