Many Passiflora species are under severe threat in their natural habitats, so it is important to both propagate & share them and their hybrids of which surprisingly few are available relative to the number named. I have to date named seven hybrids of which six are commercially available.
Propagation can be from Passiflora seed, which will be variable & will be hybridized if crossed with another species or hybrid. If vigorous, disease & virus resistant & free flowering, particular offspring may be named as a 'selection' of the species. e.g. P. 'Gillian Wren' or as a new hybrid e.g. P. 'Flying V'. If you have a free flowering vigorous plant you are happy with, propagate it by cuttings rather then seed, as seed will be variable & there is little chance of improving on the parent plant. Cuttings will be identical to the parent plant whether speces or hybrid. Existing hybrids can only be propagated by cuttings. For a number of techniques see here.
Note that some Passiflora cuttings will root very easily & others will rot very easily. Some cuttings will even take just in water without heat or rooting powder or gel. If you lose them you have not necessarily done anything wrong. Some are reluctant either to root or to grow once rooted. For example, P. racemosa will root but not grow unless the growing tip is left on the cutting. Everyone has their own technique & thanks to Jane Lindsay of UK Collection, Charlie Pridham of Roseland House UK and Ian Webb (PSI member) for their advice in helping me acquire mine. The best times to take cuttings for most species are in the spring or autumn. The phases of the moon are also thought by some to be important. In order they are Waxing from New Moon through First Quarter to Full Moon, & Waning from Full Moon through Last Quarter to New Moon. Cuttings are thought to do better when taken when the moon is Waning, particularly in the Last Quarter.
Passiflora also become hollow a certain distance back from the growing tip. Hollow sections are notoriously hard to root & prone to rot so avoid them if you can. You can however try blocking the hollow ends with lard or wax or similar. P. incarnata is a good example of one that becomes hollow very quickly....but is very easy to root instead simply by gently pulling out & planting a fresh stem, appearing usually in May, which should come out with a few inches of root.
One of the joys of the Internet is how easy it is to make contact with people from any country & then swop seeds & rooted cuttings. Some species of Passiflora e.g. P. suberosa & P. tripartita var. mollissima can be very invasive if imported into the wrong country. Please also read the Conservation link to left for information re CITES & wild collecting. If you want to post plants pack them properly - in a pot & fixed so they cannot move or dry out in transit.