Hi welcome to the forum! When you say you need to let the tank cycle, basically it already is. The cycle is a series of chemical reactions that happen through a colony of bacteria that will grow in your filter. Basically when people say cycle they mean like a scientific cycle a bit like the frog life cycle you learn about in school..... if that makes sense hope you can make the comparison.
But yeah in a fish tank it goes :
Fish poo = ammonia, then ammonia = nitrite, then nitrite = nitrate and then we do a water change which keeps the nitrate at a healthy level where as the bacteria live on the ammonia and nitrite and keep them at 0.
In a new tank this ammonia is not present so there is an abundance of fish poo and as a result ammonia with no bacteria to use it and make the water safe. At this point the fish in the tank are exposed to high levels of toxic chemicals like the ammonia and nitrite, this will stress them and leave them susceptible to diseases and in some if not most cases they can be killed by this.
So if you have fish in there now you are in whats called a fish in cycle, this means that the above process is going on based on the poop your fish is creating. Do you have a liquid based test kit for ammonia and nitrite? If not I would get one asap it will be very useful for you many times in the hobby. How ever since there is a fish in there now you will need to start doing daily water changes to keep the ammonia and nitrite levels down to a minimum this will ensure that your pet will remain healthy and in a small tank like that I dont think it will be too hard for a while. You want to change about 50% of the water each day and as for how long that depends on what the test results say, you need to keep ammonia and nitrite to as close to 0 as possible but after a while the filter bacteria colony will be able to handle it and at that point you will just need to do weekly water changes like normal
Now you said you have a plec? Is this the one in your display picture? If so that looks a lot like a gibbiceps to me, and I am afraid its going to grow far too big for your tank. Those fish get to about 18 inches with 24 inches being very common. So Im afraid youve hit problem number two, you kind of need to decide if you want to rehome this fish to someone who will be able to provide him with a tank big enough for him to grow and live in or do you want to get a tank that will be able to house him for life.
If you choose to rehome him there are possibly a few other catfish that will work in your tank, like some of the smaller species of plec like bulldog or even some of the smaller twig or whiptail catfish but the latter two are quite rare sometimes....
Personally with the above two bits of information I would take the plec back to the store or to someone that can home them properly and start a fishless cycle rather than a fish in cycle. A fishless cycle is where we use pure ammonia to bypass the fish poo to create the above cycle this way no fish get ill, stressed or die and when the cycle is over you can add fish with no worries it is really easy
I know the above looks quite bad but they are all beginner mistakes and we all make them but thats how we learn and are able to pass on our experience to new comers and make the begging stages of their hobby easier.
Hope thats helped
Wills