If ammonia and/or nitrItes rise above 0.25 then do a water change to bring the levels down. This is why testing often is helpful because the smaller the increase, the smaller the water change you have to do.
If you can get some filter media from a cycled tank to place in your own filter that can greatly speed up the cycling process. A good handful of gravel from a cycled tank can help somewhat as well, but is not nearly as good as only a small amount of bacteria live on the surfaces inside the tank. Placing the gravel in an unused nylon stocking before putting it in your own tank makes it easier to remove later. In both cases (filter media/gravel) make sure to keep both wet with tank water at all times.
Another (more advanced) method of reducing ammonia levels is planting a LOT of very fast growing rootless plants such as hornwort/foxtail, anarachis, and java moss. Plants love to suck up Ammonia and Nitrites for food, so you would have to be very careful about removing the plants slowly after about a month to prevent overloading the biological filter. Unfortunately this may require a lot more light than what most beginner tank setups have, and you'd still need to check the water parameters daily to make sure that everything was safe.