The primary thing that makes a vampire a vampire is "the blood thing". The following text provides some basic facts and some vampiric examples to assist you in creating your particular brand of blood drinker.
A human being will take 1d6 SC per cup of blood removed from them. They have about 1.5 gallons of blood (or 24 cups). Just losing 3 cups will put the typical human into mild or deep shock. Most blood donors give a pint (2 cups). A healthy human will regenerate a cup of blood in 24-48 hours.
Fangs are typically used to pierce the skin so the blood flows. The vampire then drinks it as any other person would. A person can drink a full cup of liquid in about 3-5 seconds (possibly faster if slamming it, which is uncomfortable). Some fangs are actually similar to hypodermic needles, and the vampire suctions the blood through the teeth instead; this will typically take about 30 seconds per cup of blood.
A normal human stomach can store about 3 cups of liquid; liquid digests very rapidly for a normal human (3 cups of blood might be digested in about a quarter hour to a half hour). Not all vampires will be limited to their stomachs, of course. The human body is 2.4 gallons (including meat and bone), and about 1.5 gallons of that is blood. All of a vampire's blood could come from victims (around 24 cups) or the vampires entire body could have been replaced with animate blood (around 40 cups).
I Likes It: The vampire gains nothing tangible, but may have an addiction, psychological compulsion or just a very strong desire (read, "sick in the head"). Many antihero vampires in fiction are of this sort, and are presently fighting off the desire.
Drain: The vampire suffers without it. This is a more physical addiction, and may even be a matter of survival. Suffering can take the form of unnaturally fast aging, damage, "getting ugly", becoming weak, going comatose and more.
Death: Like the Drain, but the vampire will literally die if she does not take blood every once in a while. An example might be a vampire who must drink the blood of a virgin once a year or turns to dust on the stroke of the New Year.
Demonic Contract: The vampire must take a certain amount of blood as part of a contract for power with some otherworldly evil. This is often tied to a Drain of some sort (bad things happen if the contractual obligation is not met), but also provides a more tangible enemy, should the vampire want out of vampirism.
Timeline Vampires: These vamps suck blood through the teeth with powerful suction provided by their modified stomachs. They can get about a half cup in 5 seconds. The vampire must digest the blood mystically (their stomach is no longer capable of normal physical digestion), which takes about an hour per cup of blood. Each cup provides a variable number of "points" of psychic energy based on the person it was taken from (a 25 year old human would typically provide 2 points), which can then be spent on all of the vampiric powers. The wound left by the teeth is barely a pinprick, and seals over quite nicely when the fangs are removed. Timeline vampires get power out of blood, but they also require it to survive - each night their bodies consume 1 point of psychic energy or takes 1d6 SC damage. Timeline vampires can die from this.
Dracula: Dracula uses his fangs to cut the victim's jugular open, and then proceeds to suck the blood via mouth. He is quite skilled at "slamming", and can typically get a cup per 2 seconds. He can lick the wound afterwards, sealing the hole. One cup of blood sustains his hunger for a full week. Without this, he is affected as if starving (but not dehydrating) each day past the week. Nothing else will sustain him. Normally, Dracula drinks from a different person each week. If he drinks from the same person three weeks in a row, that person becomes his thrall. Thralls are a lesser form of vampire who are unnaturally loyal to their creator.
Splattervamp: This vamp uses his fangs to rip open the victim's flesh so that the blood pours freely. Although he must ingest blood in the process, the real energy comes from the pain the victim suffers and the ebbing of the victim's life force - the faster and more painful the kill, the more the splattervamp gets out of it. Generally, the best that can be hoped for from a single kill is 10 points of psychic energy, and even a skilled splattervamp averages closer to 8 points. These points are lost at a rate of 1 point per 3 hours; after that, the splattervamp begins to lose SC at the same rate (lost SC can be regenerated at a 1:1 ratio with psychic points). Instead of dying, however, the splattervamp merely goes dormant at the "death" point (with occasional short bursts of action possible even then, if a few seconds might get him another victim to spawn a new feeding frenzy). Splattervamps tend not to last long - they are either beaten into dormancy or run out of victims soon after reawakening. In some games, 18-20 year olds may give more energy.