The fundamental concept for this instructable is to use heat shrink tubing to clamp the brush's bristles in place, and also clamp this 'casing' or ferrule to a handle. Essentially, replacing the crimped metal sheath of a store-bought brush with the plastic heat shrink sheath.

I'm sure that you will be able to take the simple concept and make it your own. Creating from your own materials and to your own required specifications. But i will show my specific Materials and Methods in a few steps that follow.

Before that though, here are the materials you will need (pictured also):
hair of some sort for the bristles
heat shrink tubing (a.k.a. “heat shrink”; or just “shrink”) used in electrics and electronics
(possibly) glue
wooden dowel or food skewers
scissors
point heat source such as a cigarette lighter
sewing thread.

Background (You don't NEED to read this)
There are a few instructibles on making brushes. I've added mine because I think it's easier and quicker, and I can add something to the approach as well as simply showing a method that's not represented so far.
There's no glue or cutting holes or slots into handles. The materials are cheap, and you may already have them.

Step 1: Prepare Your Bristles

Bristle Source
Do you have long hair you're willing to sacrifice pieces of?
No? Then do you have access to someone (sister, wife, etc.) who sleeps soundly? :)
I joke. But i do foresee a lot of pets with missing tufts of hair.

Horse hair – if you know people with horses, this is a good source of longer hairs. Though the longer pieces from a horse's clipping (yes, they get haircuts) is from the tail or mane, and is thicker hair.
     I have long hair but only cut it once every 6 – 12 months. So I get a good long lock off. Try to keep it together when you cut it – splitting it up is easier than trying to put a bunch together.
     The ideal in precision paintbrushes are hairs that each taper at their tips. You may be able to achieve this using some animal hair.
     'Fresher' hair will be easier to manipulate. Though it's the natural oils etc. which make this so, and you may wish to wash the finished brush before use to remove these 'additives'.

Orientation
If you're using natural (mammal) hair, remember that it has a 'direction'. Although the brush i'm making here is most useful as a paintbrush, a brush isn't a paintbrush until it has paint on it. So create your brushes with their purpose in mind. The reward for creating with intent is a tool that's a pleasure to use. In this case, the scales on the hairs could point 'up' the handle of the brush to better 'scrape' if it's a brush to sweep (say dust) away, or could point 'down' the brush for a smoother application of paint.
     A similar approach can go for hair / bristle selection.

For this example I'm using human hairs, cut to approximately 60 mm (2 ½ inches) long from a longer lock.

Step 2: Fixing the Bristles in Place

Select a bunch of hair to fit into the heat shrink ferrule. If you're sliding the hair straight in, get as much in as possible without too much effort. Or use my alternate method described below. Then heat only the section of shrink tube that is covering the hair. It will tighten down and clamp the hair in place, taking up the little space you couldn't fill. The further into the heat shrink tube you can have the hair, the more area there will be clamping down on it holding it in place. A small flame such as that of a cigarette lighter is best for this local heating.
Because we're using a ferrule that tightens down on the bunch of hair (bristles) when it shrinks, you may wish to use no glue to hold the bristles in place. This is especially unnecessary if you're doubling the hair over in a bend (as I describe below). You could certainly change the process slightly and ass glue if you like, but i'm going to show my process without glue. If you do use glue it's to hold the bristles together as a bunch (rather than hold the bunch to the handle), and you would apply glue and let it set or dry before continuing. Doing this lets you best control where on the bunch of bristles the glue goes. You want as little glue as possible, restricted as much toward one end of the bunch of bristles as possible (so that there's space between bristles to 'hold' paint. Don't let glue 'seep' along the bristles by capillary action. Wood glue (white glue) is best but watch for water solubility.
My method for getting the hair into the heat shrink easily and compactly is to tie sewing thread around the bunch of hair, and pull the hair into the ferrule using the thread. The thread is tied in the mid point of the hair bunch. And the bunch of hair should be half as much as will fill the heat shrink ferrule, since it doubles over when its middle is pulled into the ferrule.
This has a few favourable consequences. First, a single hair that's doubled over is less likely to fall out of the brush (to mar the applied paint job). Second, when the heat shrink contracts around the (larger) bend in the hairs it shrinks on either side of the bulge and locks it in place better than otherwise. It also means handling longer hairs which is less fidgety. And i'm not that fussy about the hair's direction when i'm making 'quick and dirty' brushes.

Step 3: Adding a Handle

Slide the heat shrink ferrule over a suitable handle and heat to affix them together. A cigarette lighter works well as a small heat source. Pass the section of heat shrink tubing through the flame tip gently until the tubing clamps down.

We're producing quick, somewhat dirty brushes here. But that just means our intention is to do so. It doesn't mean we can neglect reasons for everything we do. So you could turn beautiful handles on a lathe, but to match the 'quick' and 'cheap' themes i'm using rough materials that I can find ready-made for my handles. But i'm still considering every aspect.
A good handle is long enough to contact two places on the hand when held (at least pencil length). It won't dissolve or degrade if it meets paint solvent. And it won't fall apart easily. To match the shape of the heat shrink ferrule, i'm using round wooden 'sticks'. For the size brush i'm making here, a kitchen skewer is perfect. However dowels from a hardware store etc. come in a range of sizes and you'll probably find one to suite.

The heat shrink ferrule may not be sturdy enough for your application. In a good paintbrush only the hairs bend and move which allows predictability etc.. You could consider slipping a second layer of heat shrink over the first. Or adding hot-glue over the ferrule. It may be easier to do this before adding the handle, or afterward.

Step 4: Shaping the Brush Head

Using a pair of fine scissors, trim the head of bristles to the shape you require. If you don't know what that is, a starting point is the 'paintbrush' section of the Wikipedia article on “brush”. Also important is the length of the bristles. The brush will be stiffer with shorter bristles, but very long bristles are for special applications. The joy of making your own brushes is that you can customize everything and create a tool precisely for your application. But also that you can experiment and find the perfect characteristics, especially when it's cheap to do so.
The heat shrink is cylindrical and obviously creates round brushes. You could potentially 'flatten' the bristle set by some clever method of clamping down over the bristle-containing heat shrink. Perhaps with something as simple as a paperclip, or other paper clamps.

Step 5: Concept Tweaks, Applications, and Other Uses

A brush applicator for very thin (non-viscous) cyanoacrylate glue can be made by following all the steps except for adding a handle, and then sliding the heat shrink ferrule over the pointed nozzle of the glue applicator bottle. By squeezing the bottle, the bristles are flooded, and the glue can be brushed onto surfaces for adhesion or for woodworking finishes. (Look out for an instructable on this coming soon.)
You could also create a brush from extended heat shrink tube, and simply fill the tube 'handle' with the agent you're applying, allowing it to flow through the bristles. You would have to be using a 'paint' with very fine pigment particles (or ink). Though this may lead to dripping. Let us know if you try this.
There are a number of clever paintbrush designs for creating patterns, or combining 'units' to vary overall brush size. You could likewise combine your brush 'units' by whatever ingenuitive means you come up with. Here's an expose on 'The Paint Evolution' by culdesac - http://www.designboom.com/weblog/cat/8/view/18049/culdesac-the-paint-evolution-for-valentine.html/