Both are disseases that unlock an extra skillline to level.

I never played a werewolf, so I'll only explain the vampire.

Vampirism is a dissease. This means you have a constant thurst for blood. It is expressed as a debuff that makes your healthregen slower and makes you more vulnarable against fire. But it also makes your vampire abilities easier to use. There are 4 stages, and the higher the stage, the more severe the dissease (and the cheaper the vampire abilities become). You can reduce this effect by feeding. (stealthing to a person from behind and feeding on thier blood while hidden). Each time you feed you go one stage.

The vampire abilities are three extra skills. A drain that stuns foes and steals health and heals you. A skill that stealth yourself for a brief time and an elite that deals point blank AoE damage. The more important are the passives. While some are just to counter the bad effects or to infect other players, one is important, cause it increases your stamina and magica, which increases your dps. So in short a vampire deals more dps, but has lower health regen and is vulnarable for firedamage..

The way to obtain the dissease is the same for vampires and werewolfs.
There are two ways.
At designated spots in the level 38-45 map of your allaince, are places where vampires (bloodfiends) and werewolves spawn that can infect you. They only spawn at nighttime (in game) and only at specific moons (different for vampire and werewolves). If they are killed they don't spawn for another night. (and the window they can spawn is 1,5 day in total). So this way is pretty hard.
Another way is that a player with the dissease takes you to the vampire shrine or the werewolve shrine (in the same 38-45 map) and bites you in front of it. This will turn you into one. After that you need to do a level 38 quest (but your skills are scaled to it, so it is doable at most levels) and you unlock the skillline.
Players can only bite another player once they reach level 6 in the skillline and there must be 7 days between each time they infect someone.

If you play on PC, then it is easy to find someone to bite you. In general people charge 2-5k for a bite. In most guilds is a rule that guildies are bitten for free.

Om the consoles, As the game is new, as getting the bite from the rare spawns is very rare and as there are not so many vampires/werewolves around yet, it is a different story. I've seen people offering up to 75000 gold and even real money for a bite. As it was with the PC, the price will go down over time.

Atleast vampirism is something that gives a more challenging gameplay, I would recommend waiting till it is not so rare anymore. You learn the game better first and you save a lot of money.