Vampirism is a mod that adds a whole new way of playing Minecraft. You may have previously spent a lot of time avoiding mobs, but as a Vampire, you will develop a thirst for killing :)
There are currently two ways you can go: You can become one of these powerful and bloodthirsty vampires or join the other side, train yourself in defeating those cruel vampires and maybe learn to take advantage of their powers.
Don't forget to check out the guide book (if you have installed Guide-API(1.12) or Guide-API-VP(1.14+)). If you lost your initial one, you can get a new one by combining a normal book with a vampire fang or a human heart.
First steps - Vampire
To become a vampire you have to be bitten by a vampire. So either let them hit you on purpose or just wait until it happens by accident. When they hit you there is a chance, you receive a potion effect called "Sanguinare Vampiris" which lasts about a Minecraft day. After the potion has ended, you become a vampire.
In case you don't want to become one, you can always cancel the effect with a milk bucket.
Alternatively you can right-click with vampire fangs in you hand to inject some blood into you and get the same effect as above.
Once you become a Vampire, one of your main sources of blood (at least the best source) are villagers and you should find plenty of those. Watch out though, Vampire Hunter's will now attack you and try to protect the villagers.
You will already notice that you do not feel very good in the sun, but the sunlight won't hurt such a weak vampire as you are at this point.
As a Vampire, you need to watch how much blood you have. Suck blood by pressing 'V' (Check the key bindings) from villagers and some animals to get more blood. Extra blood will be stored in Glass Bottles/Blood Bottles on your hotbar. You might even be able to suck blood from other players, as long as you are coming from behind so they can't defend themselves. If you bite a mob, that does not have blood, you will deal some damage to them.
In the beginning you will be a level 1 vampire (the level is displayed above your XP-level) and have improved speed, health and strength.
To get to higher vampire levels you have to perform different rituals. As you advance through levels your abilities improve, but some disadvantages like sun damage might appear.
First steps - Hunter
To become a vampire hunter you will have to find a village, in which a "Vampire Hunter Trainer" lives. You will find some garlic plant behind his house. Use them to craft a "Garlic Injection". (You might want to replant the garlic since it will be useful in the future.)
Go inside the trainers house and use the special chair inside to inject your that garlic vaccination. It will make you immune to the Vampire's poisonous "Sanguinare Vampiris" bite.
This is more or less the only advantage that you will have at that level. But you can train yourself to become stronger and learn some useful skills.