I completely agree with Michael, if your tank filter in the 2.5 gallon has been cycled(most likely if you do not have ammonia) the quickest way to cycle your tank is to use the same filter on the new tank, and throw in the frogs. Honestly if they are currently in a 2.5 gallon aquarium, I would advise you to throw the frogs in the large tank regardless of whether your old filter has cycled or not.
I didn't want to read the article, so I'll just summarize cycling. It's the process of cultivating two types of bacteria that neutralize the chemicals your fish produce in the tank. One type of bacteria converts ammonia(most deadly) to nitrite(somewhat deadly). The other converts nitrite to nitrate(least deadly). Your filter cultivates the bacteria by providing an ideal place for it to live. Aquarium filters can have a number of different purposes, but we're currently only worried about bio filtration(cultivating bacteria in filter). Your filter probably has a porous pad that is called your bio media. This is where the bacteria lives. This is why it may be faster to just filter you new tank with your old filter. I recommend leaving the old filter in the new tank for at least 2 weeks before taking it out to "seed" your tank with beneficial bacteria.
If you are doing fishless cycling(nothing alive in tank, and only dosing ammonia) do not do a waterchange until you only have nitrates.
If you are cycling with fish do a waterchange every time ammonia is over 1 ppm, nitrite is over 3 ppm, and nitrate is over 40.
Once the tank is cycled I recommend doing a waterchange once a week, or whenever the nitrate reaches 40.
No need to scrub the tank with a toothbrush. The only thing that really matters for the frogs themselves is the water chemistry(ammonia, nitrite, nitrate). Your tank could look disgusting(my tank has a ton of mulm on the bottom from plants) but have really good water quality. Make sure you have an ammonia, nitrite and nitrate test kit.
Also this may seem counter intuitive, but do not scrub the filter media, or clean it with chlorinated water. When I clean my filter, I do it in a bucket of dirty tank water after I've done a waterchange. The bacteria I was talking about earlier lives in your bio media in your filter, and you can kill it if you clean it with chlorinated water.
If you have any questions feel free to ask