The other day my post was on Macro photography. I am sure the impression was given that this is a highly technical field, and it can be. Here is a simple method that works fine in many instances to get a taste of what is possible.
Have a look at the closest focusing distances of the lenses you have. The shot above was taken with a 70-200mm lens, not what you would think it was intended for, but it works, even at distance of five feet away with a bit of cropping.
Wide-angle lenses are even better. You can get within millimeters of a plant or a compliant bug.
Sure a Macro/Micro lens is preferable and there is less cropping but while you are figuring out if you want to invest in more gear, experiment with the close focusing of your lenses. zoom or prime lens, it does not matter.
My only recommendation is if you do decide to spend money, be wary of close-up filters. They can be expensive and may not deliver the quality you would expect. I have never tried using bellows, I do use extension tubes with a 105 mm macro lens.
Experiment with the lenses you have, its worth the effort.