How to cycle a fishtank

[Mentat]

Your two requirements can oppose each other when it comes to cycling an aquarium. Also, the presence of live plants requires different approaches.

The fastest is by using media from a cycled healthy tank. If no cycled filter is available; then adding a culture of live bacteria to aquarium together with the aquarium inhabitants is only other option. As long as the bacteria in package are fresh and alive, they will populate filter and will feed off the ammonia produced by fish and adjust their population accordingly.

The easiest is again to add filter media from a healthy cycled tank. Or just add a very small number of your sturdy fish (can't do this with ammonia sensitive fish) and let tank cycle itself. It will take around a month for it to happen; but you can cut that in half by using a product that inoculates filter with dormant bacteria like Seachem Stability.

If you have no live plants, can add aquarium salt (1 tbs. per 2.5 gal.) to reduce the damage from ammonia/nitrites during cycling. If it's a heavily planted aquarium, the plants will consume most of the ammonia; but will still have a nitrite spike during cycling.

Do not use any ammonia neutralizing product like Amquel during cycling. They are very aggressive removing ammonia and nitrites leading to bacteria population starving death and the cycle to be interrupted. That effect will continue until the product is removed with water changes or decomposes away, making for a very long cycling period. Hope this helps and good luck !