There are several times throughout the game where Kaepora Gaebora, the infamous owl, will try and talk to you. His texts can be rather long and annoying, especially after you accidentally say you would like to hear his text again. However, there are numerous methods and techniques used in order to skip many of his texts.
In some cases, the simplest solution to skip talking to the owl is to simply avoid his speech triggers. A few examples of where this can be done are for the owls near the entrance to Lake Hylia, near the entrance to Gerudo Valley, and an owl in the Lost Woods if you are heading to Goron City.
If you are able to perform either a Ground Jump, Superslide, or an ESS through the owl's text area, you will skip it, as he is not able to talk to you while you are performing these tricks. Once you are through his text trigger, it is safe to release the trick and continue onward. Examples of owls you can do this on include the owl in the Lost Woods if you are heading to Saria, and the owl at the start of Zora's River. Note that this can even be done with the very slow recoil ESS off rocks or torches, but is probably slower than talking to the owl anyway.
It is possible to skip past owls if you alternate between either two C-button items or a C-button item and a sword (Note that this will not work with all C-button weapons). By alternating between these two quickly you will never fully use one of the weapons, only pull it out a bit before starting to pull out the other item. While this is occurring, the owl is unable to talk to you, so keeping it up through his speech trigger will allow you to skip him. However, this trick requires precise timing and rhythm, not so much speed or button mashing. It is generally considered a hard trick to pull off. The best chance of being able to do it is with the sword and a deku stick. It is useful on the very first owl outside of Kokiri Forest, because at this point in the game you will not have explosives to do a ground jump or superslide, and there is nothing to get an ESS off of.
The owl that sits in a tree near the stairs to Kakariko Village can be skipped without the use of any items at all, thanks to a sign next to the stairs. If you get close enough so that the action icon changes to "Check", you can avoid triggering the owl's speech. This can usually be done with a backflip or sidehop into the "Check" trigger range. Once you are next to the sign, you must get out of the owl text trigger. You can either edge along the wall until you are out of the check trigger, or you can pause/unpause and do a backflip or sidehop on the next frame to leave the check trigger. Pausing allows you to backflip or sidehop without reading the sign.