These collett's are available in a variety of Imperial and Metric sizes, which you'll match up with the shank of the bits you're using. If you're using a 1/4" collett, you'll need bits with a 1/4" shank.
For cutting, you'll most likely be using End Mill bits. They're similar in design to drill bits, except the have blades on the side to allow for horizontal cutting, rather than simply plunging up and down. The two parts of the bit are the shank and the cutting area. Insert the shank only into the collett leaving the cutting area exposed. For ideal results you'll want to use the shortest bit possible for the job as the longer it is the more tension is taken up by the bit and the more likely it is to snap.
There are many varieties of bits available, and specialized bits for any material you'll be cutting. For long bit life and the best cutting, you may want to consider some good carbide bits. In a pinch, the bits at your local Home Depot will work, but they won't last as long or cut as cleanly.
You'll find that there are many types of end mills available. The two main types are upcut and downcut. The upcut pulls waste out of the cut, while the downcut does the opposite. The downcut type leaves the top surface cleaner, while the downcut leaves the bottom cleaner. It should also be noted that the upcut endmill bit pulls up on your material so it's more important to have it held down securely.
For cutting wood, either can work, but for plastics and other materials you may want to go with an upcut to prevent wasted from melting into the path it left. There are also different flute patterns (single, double, etc.) which are useful for better cleanup and finishes.
A straight end mill bit is useful for most cutting, but if you're planning to do any relief or 3D work, you can also consider a ball nose endmill bit. This is simply an endmill with a rounded tip, producing a smoother finish than the flat tip of the traditional endmill.
For finer detail, there are also engraving bits, which taper down to a point at the end, using different angles. These are great for text and very fine detail work, but keep in mind they're not designed for lots of straight cutting like end mill bits and they'll break easily if you ask too much of them.
Also popular is the V-Bit, which allows you to create a beveled effect of the edges of your cut without having to build it into your design. These are very useful for lettering and for borders.
You may also want to fave a fly cutting/planing bit on hand if you have a lot of surfacing planned. This bit has a flat bottom designed for skimming the surface of your material. You can get them in very wide diameters, cutting down your work time, but again, it is not an endmill bit, and not for deep cutting.
Those are the basics. Of course there are many other specialty bits available, such as drag knife bit to allow your CNC to work like a vinyl plotter.
Here are some starting tips to help you get going (mostly for endmill bits)
1) Start out cutting the same depth as the diameter of your bit. (quarter in diameter, quarter inch deep.) As you get more comfortable, try cutting a little deeper. You should never cut more than 4x the diameter of your bit.
2) Make sure that you take the exposed length of your bit into account when cutting. For example, if your bit extends 2 inches from the collett, you cannot cut 2.5 inches deep.
3) Tighten the cap over the collett, after the bit is inserted. Make sure the collett is flush with the bottom of the cap.
4) Your bit should spin straight. If you see it wobbling when you turn on your spindle, it is not inserted correctly.
5) Consult your bit supplier's charts for recommended feedrate/RPM for diferent materials. Wood, Acrylic, Aluminum and other materials all have their own needs for ideal cuts.
6) Use the shorteset bit possible for the cut to decrease possible deflection.
7) Use the largest diameter bit possible to cut deeper and reduce work time.
8) Keep your bits clean after use to extend tool life.