Before you attempt to harvest trumpet vine (Campsis radicans) seeds, consider that the vine's seedlings sometimes take a long time to bloom -- up to 10 years. Because the vigorous plant, hardy in U.S. Department of Agriculture plant hardiness zones 4 through 10, suckers freely and spreads quickly, another gardener probably will be more than happy to give you a division instead. However, if you still wish to try seeds, they aren't difficult to locate.
You will find a trumpet vine's seeds in its bean-like pods which can vary in length from 2 to 6 inches. Two or three months following the plant's bloom-time, those pods should age from green to gray-brown when the seeds enclosed in them are mature. This usually happens in early to late autumn. Pick those pods after their color has changed from green to brown but before they crack open.
Each seed is a roughly circular flat brown disc about 1/4 inch in diameter enclosed in a transparent, tissue paper-like membrane. That membrane flares out into wings on either side of the disc, helping it float on the wind.
After cracking open a pod and extracting the seeds, spread them on a paper towel indoors to dry, keeping them at room temperature. When one week has elapsed, slip the dried seeds inside a paper packet and store that packet inside a lidded glass jar in the refrigerator.
In late winter, or about two and a half months before you wish the seeds to germinate, remove them from their packet and soak them in water for 24 hours. After stripping the winged membranes off of the seeds to leave only the discs, place the stripped seeds inside a plastic sandwich bag along with a handful of damp seed-starting mix. Zip up the bag, place it in the refrigerator, and keep it at temperatures between 41 and 50 degrees Fahrenheit for two months.
When the two months have passed, remove the bag from the refrigerator and extract the seeds. After filling a flower pot or other seed-starting container almost up to its rim with moist seed-starting mix, press the still damp seeds into the surface of that mix without covering them with additional mix. If you top the container with plastic wrap to keep the mix moist and place it where it receives temperatures near 70 degrees F, the seeds should begin to germinate within two to three weeks.