A Brief Guide to Safer Bloodletting

There are only really two methods which are really suitable, IMO (barring things that require you to use your ritual dagger to draw blood and the like). One is the use of needles or sterile lancets and the other is scalpels.

You can get hypodermic needles and syringes from any clinic, pharmacy/chemist, or hospital that is part of a needle exchange program (the UK has an extremely good program of this sort). They will also dispose of used needles. Lancets are provided to diabetics to allow them to test their blood.
Suitable scalpels can be acquired from art shops; boil them if you want extra sterility. Scalpels are much better than knives, because they are so much sharper, thus making the whole thing a lot more painless. Razor blades are also suitable.
For needles, I prefer to take blood out with a suitable size of syringe, although it is possible to set up a catheter, or use a lancet or needle (sans syringe) to pierce a vein, and suck from it directly.

The best place to take out blood with a needle is from the vein in the crook of the arm. It's best to get someone to teach you how to do this. You don't want to puncture an artery by accident, or hit a nerve (now that HURTS), or end up with bruises all over your arm. Make friends with your friendly local junkie. The needle kits will probably also come with some instructions for finding veins.
This will result in no scarring, and any marks should heal up within a day.

Obligatory Safety Notice:
The use of clean and sterile works is as important for magicians and vampires as it is for drug users.
It's not a good idea to share needles, however clean of disease someone might be - it's rather easier to catch things from needles than it is from drinking blood (assuming you don't have ulcers).
It's only advisable to use a needle a maximum of three times before throwing it away; they blunt rather easily.
DO NOT inject someone else's blood, as blood of an incompatible type can and has caused serious problems.

Scalpels tend to cause rather more scarring than needles, as you have to hack through quite a bit of flesh to get at your veins.
Always make a transverse incision (i.e. across the vein, rather than down it), as these heal up more easily, and are less likely to cause severe blood loss.
Don't cut too deeply, as you may run the risk of severing tendons.
Some scarring is probably going to result (I still have scars from cuts of this kind made 6 years ago), so make cuts somewhere innocuous.
If you don't need much blood, the back of the hand is surprisingly good, as it heals easily for some reason, you don't have to cut very deep, and no one pays attention to cuts there.
If you're worried about accusations of mental instability, DO NOT cut your forearms. Upper arms are harder to find a vein in, but at least they don't scream suicide attempt.
I have been told that Vitamin E creams, easily available at your local pharmacy, help heal skin so that scarring doesn't occur.

Some people recommend ankles and feet, but that can be uncomfortable if you wear shoes.
You could also try behind your knees, which I've heard recommended by some.

I don't know that much about the best places to use a scalpel, as I always use needles except in emergencies.
If you don't have a local needle exchange, dealers in drugs for IV use will often be able to sell you the necessary equipment.
If it ain't sealed in a sterile wrapper, don't use it.

If you need to use a dagger, it is advisable to boil it, or at least dump a load of medical alcohol over it first.

If you use a scalpel or knife, you'll probably want to have some cut medication handy to help it heal up faster and more painlessly, and to help stave off infection. We recommend Germaline, which has both antiseptic and pain killing properties. It works for lizard scratches, at any rate, and they're a good deal more septic than a cut with a sterile blade. It's also a good idea to swab the area you're about to cut with alcohol - many distributers of needle packs include a box of alcohol wipes with them.