Introduction
Vectorising people was a huge hit a few years ago. It still is a bit, but not so big as it used to be. When you vectorise a photo, what you actually do is use single-color shapes to redraw the photo, but this time using minimal colors for the shading, making it look like only a handfull of colors were used for the photo.
In 2006, a movie also came out in this vector-style called A Scanner Darkly. In this film, black strokes were also used. Some considder that strokes are not vector, but in fact there are 4 different versions of the vector-style. They're more interpretations than styles, since styles shouldn't be followed through rules.

There is the simple method where you work with but a few colors and no strokes, then there is the version where you try to replicate the photo using shapes and LOADS of colors. This method tries to use THAT many shapes which will make you doubt it's a vector graphic. Then ofcourse there's the method where you also add strokes to simulate comic-graphics and finally there is the method where you also use gradients to enhance the colors and depth.
In theory, there is no set style and it's not based upon rules, so you're free to do whatever you want.
For this tutorial, I must advice that you know how to use the Pen-tool. You CAN vectorise without it, but it's basically the vectorise-tool, so you better learn it. Other then being usefull for vectors, the Pen-tool is a great tool and certainly my favorite one!

Vector, is perhaps also a very strange name for such a style due to the fact that vector is also the meaning of the use of geometrical primitives like curves which are based upon mathematical equations. In other words, when you enlarge a vector image, you will not get the blurry fuzzyness that pixel graphics have. Programs that use vector graphics are Adobe Flash and Adobe Illustrator.

Getting started
In this tutorial, we're gonna vectorise a person, since that is perhaps the hardest thing to do, because of the shading, colors and the dangers of the Uncanny Valley, which will make your vectorised person look like an alien.
For this tutorial, I used a nice stock-photo from Lacey Chabert. That girl has such a cute smile and amazing eyes... anyhow...

Press CTRL+J to duplicate your photo-layer and go to Image>Adjustments>Posterize which will open a window that will devide your photo into pixelated areas. This will help you select your shapes. Select the box that says preview and choose a setting where you think you got enough visible sections. The higher the amount, the more shapes you're gonna have to draw.
For my photo, I used a setting of 6.

Preparing the document
What we're gonna do now is prepare your document for realisation of the vector. The process of a vector takes a long time, especially for a beginner. This is one of those things that just takes a lot of time. Luckily, time equals quality, so the more time you spend on it, the better it gets. But in order to spend time on it, we want to have a document that's pleasant to work in.
Right now you should have 2 layers; your photo and the posterized version. What you need to do now is make a new layer with your final or perhaps temporary background. After that, when you're gonna start working, make sure you're gonna do all the base-shapes first and the mask the shading-shapes with the base-shapes using CTRL+G. Confusing? No need to since we'll be covering that more later.

Beginning your vector
I started off with the shape of the skin. Remember that the parts that won't be visible, because hair or clothes will be overlapping that, CAN be visible now. Look at my image above and notice how the visible areas are perfectly shaped and the areas that won't be visible are messy. This is because you want things to overlap and not match. If they overlap, you will not notice the annoying space between them that looks like a black pixelated line. Trust me!
I used the Pen-tool to select the shape of the skin, then used the Eyedropper to select a color of the skin using the original photo-layer and filled my selection with that color.

For the hairs, I did the exact same thing. Notice how I did the entire outline of the hair but forgot the parts that are covering her head. That, we're gonna do next when we use the same color, but a new layer to create this shape.

Continue along with the clothes, each putting every shape and color on a new layer. This will be important later. You can also start giving them names like "skin", "shirt" or "hair", if this will make it easier for you. If you get lost a lot in your PSD's, I really advice doing it. Some vectors can have over 200 layers.

Shading
Now return to your skin-layer and this time open your posterized layer and select the lightest shade on the skin. After that use the Eyedropper again to select a little darker color on the skin of the original photo. Fill this selection on a new layer above the skin-layer and press CTRL+G to make sure that everything that's larger than the base-layer, will be invisible. This way, you can be sloppy with the invisible areas.

Continue with the other shades and also other things like birthmarks, moles and eyebrows. Again, each time, making a layer above the base layer and using CTRL+G to mask it.

Up next is the hair. it will look good if you use all these small curvey shapes. Remember that you can also zoom to make the selecting easier.

Finish up with the clothing just as we've done before...

The Eyes
Then onward to the eyes. Probably the most trickiest thing on the whole face, because it determines whether or not your face looks real.
Start by outlining the shape of the eyes with a black shape and finish it off with the shapes of the eyelashes.

Then fill the eyes using the same techniques we used before. Notice how, this time, using the Eyedropper for the colors of the eyes will fail drastically, because you will notice how the eyes will appear much darker then they should be. You can cheat a little here by making the eye-white actual white.

The last few steps
Finish up by drawing the mouth beginning with the thing that is behind everything, the lips and outline of the mouth. After that, move on to the inside of the mouth including the already placed shades and finish up with the teeth. Be wary not to make the teeth perfectly white. That would not look good.

Conclusion
There you have it. It may have took you a lot of time, but now you have your awesome vectorised graphic. Maybe it's your first and you're so happy you finally started this? If that's the case, I highly recommend trying other things like environments, objects or maybe more people! If you think you got a nice vector (not the photo I used) post a link to your vector in the comments and if it's nice, I'll implement it into the tutorial!
Thanks for reading and your patience!