When fletching natural feathers, we recommend either a solvent-based glue or a double-sided fletching tape. We do NOT recommend using any type of instant glue as it absorbs into the base of the feather and will not provide good adhesion.
The benefits of using a double-sided fletching tape, such as Bohning's Premium Fletching Tape, is that you can shoot immediately after applying it - you don't have to wait for it to dry or cure. Tape usually does not expire. However, typically you get a stronger bond with glue than with tape.
Bohning's Fletch-Tite Platinum is a solvent-based glue that we recommend for feathers, vanes, and tapered nocks. It works with any type of shaft including cedar, carbon, aluminum, fiberglass, and even wrapped and painted shafts. Aluminum and carbon shafts do need to be properly cleaned and prepped before fletching though - read more here. When using Fletch-Tite Platinum, keep the feather/vane in the clamp for at least 5 minutes to allow the glue to dry, and wait at least 24 hours (48 hours is best) for the glue to cure before shooting.
Fletch-Tite Platinum provides a flexible (non-brittle) bond that absorbs shock. When shooting into a target repeatedly it does not crack or become brittle as instant glues have a tendency to do. Along with the aforementioned applications, we recommend using Fletch-Tite Platinum on the tip and tail of vanes or feathers for best adhesion. Platinum is easy to clean from jigs: simply scrape the glue off with your fingernail. It is best to fletch with Fletch-Tite Platinum in low-humidity - if you need to fletch on a humid day, consider doing so in a well-ventilated room with air conditioning or a dehumidifier. Do NOT store Platinum or any other solvent-based adhesives in the refrigerator - instead, to prevent glue from drying out prematurely, ensure the cap and tip are tightly sealed and store inside a plastic bag or plastic container.
For more basic fletching instructions and tips, check out this article.