Passion Flowers actually comprise a family of several hundred varying species of flowering perennial plants.
The leaves of passion flowers are used to brew an herbal tea with a unusually pleasant, very mild taste, The taste doesn't really resemble anything else I can think of - other than an earthy green and grassy taste. If that's not your cup of tea, it is sometimes blended with Chamomile or Lemon Balm. Flavor enhancements such as honey, sugar, stevia can also be added.
Folk Lore assigns a number of healing and therapeutic properties which include alleviating digestive track spasms and cramps, relief from menstrual issues, anxiety, as a sleep aid and tranquilizer, to treat ulcers and gastrointestinal problems.
Medicinal Properties of Passion Flower
Folk Lore claims it has a relaxing effect. Science has substantiated that claim in a number of studies. 
It is useful for gastrointestinal health and helps decrease ulcers 
Passion Flower boosts the brains levels of Gamma-Amino Butyric acid (GABA). GABA acts as a neurotransmitter in the central nervous system. It inhibits nerve transmission thus calming nervous activity. It is basically a natural tranquilizer and an effective sleep aid. 
Passiflora incarnata was also proven effective as an anti-anxiety treatment when tested against the widely prescribed anti-anxiety medication oxazepam. The researchers stated that "Passiflora extract compared to oxazepam is an advantage." 
Passion Flower Tea Recipes
To Passion Flower use 1 teaspoon of dried crumbled leaves for every cup of Hot water. Pour the hot water over the leaves and allow it to steep. I like to add some stevia leaves which sweetens it a tad, they meld together well. You can also try Honey, lemon balm or other herbal flavorings. If using Fresh Passion Flower leaves, crumble or bruise them first, the taste will be a little stronger, if this is how you like that's dandy - if not reduce the leaf to water ratio.
Sun Tea is also very simple, about 1/4 to 1/2 cup of leaves per every cup of water. Pack them in a pitcher with a lid or a jar and sit it in the hot sun for several hours.
If you are using dried leaves, they aren't as potent as the fresh so you'll need to bump up the leaf to water ratio, it's not an exact science just use your judgement.
Infusion process which works well with fresh, as well as dried herbs. Bring water to a boil, add 1 teaspoon of you dried ingredient per cup- - seep it in the water to allow the flavor to permeate the liquid. If you're getting into herbal teas you might want to consider getting a mesh ball, basically a metal tea bag.
Another method of making an infusion is to add a cup of dried herbs to a quart jar. Pour boiling water over the herbs to the top of the jar. You should also place a metal spoon or utensil in the jar when you are pouring the hot water if you are using glass. The metal will absorb the sudden heat and prevent the glass from shattering. Remove the metal utensil and cover the jar tightly with a lid. Let the herbs steep up to 10 hours and then strain.
Warnings and Cautions associated with Passion Flower.
Passionflower is used for anxiety, insomnia, gastrointestinal problems related seizures, hysteria, asthma, symptoms of menopause, attention deficit-hyperactivity disorder, palpitations and irregular heartbeat, high blood pressure, fibromyalgia, pain relief and sometimes relieving symptoms of drug withdrawal. Not all the properties attributed to it are borne out - some are folk lore and Old Wives tales while others are proven and scientifically valid.
Up till the late 1970s Passionflower was approved as an over-the-counter sedative and sleep aid , but it was taken off the market because its safety and effectiveness was unproven.
Due to its sedative effect, passionflower may cause drowsiness and dizziness. If you're already a tad dizzy - it could make you a little more baffled. Never use passionflower if you must operate machinery or drive.
It is used to treat palpitations and irregular heartbeat , in rare cases it can actually cause palpitations and irregular heart beat. Excessive or long term use can cause liver problems.
References / Footnotes
1. Passion Flower (Passiflora incarnata L.)--a reliable herbal sedative
2. Manufacture of Standardized Dried Extracts from Medicinal Brazilian Plants
3. Pharmacological studies in an herbal drug combination of St. John's Wort (Hypericum perforatum) and passion flower
4. Passionflower in the treatment of generalized anxiety: a pilot double-blind randomized controlled trial with oxazepam.