1: Cabinet design: 

Vas is the woofers  "equivalent volume" and is given in the data sheets. 
Qts is the woofers "Q-value" and is given in the data sheets. 
Fo is the woofers "free air resonance" and is given in the data sheets. 

Closed box formulas: 
Closed boxes are often used in designs who have the ambition to sound "naturally" , however it may be hard to make the loudspeaker able to handle the deepest bass tones, especially if the box is small.. 

The volume is calculated with this formula:  

And the resonance frequency : 
 

Vented box (bass reflex) formulas: 
Bass reflex boxes are the most commonly used design in reasonably priced loudspeakers, this because it is easier to make the loudspeaker handle relatively deep bass tones especially if the box is small, the downside is that the bass sometimes tend to be less "tight". 

The volume is calculated with this formula: 
 

The length of the tube is calculated with this formula: 

L is the length of the bass reflex tube (in meters). 
You may use an adjustable tube and when the design is ready you simply replace it with a more rigid tube, and fixate it carefully to the box. 
D is the diameter of the tube (in meters).  
Choose the diameter as large as possible, not to interfere with the depth of the box. 
V is the volume of the box (in liters). 
F is your chosen frequency , here is where you shall use your ears (and a spectrum analyzer). 
Many people use the same frequency as the woofers or the box self resonance, the tube will work together with the resonance from the woofer and will give a sound that will appeal to all disco or car-stereo lovers -simply don't do that!

Start with an adjustable tube and fill it with damping material, measure the frequency response of the loudspeaker, remove the damping material from the tube and try to adjust it to increase the frequency response in the bass region by some Hz. Don't overdo it, 10 Hz or so in extra bass depth is what you may expect from your bass reflex design. 

2: Filter design: 

Filters to a loudspeaker may be of active or passive type, active filters are used before the power amplifiers and you shall use one amplifier for every loudspeaker element. Passive filters are normally placed inside the loudspeaker box and works with the high power signals delivered by the power amplifier.

Active filters have many advantages before passive,  phase errors are minimized and the filter slope can be designed more steep with less distortion as a result. The main problem is that it requires one power amplifier per element and a lot of cables. Passive filters for low frequencies also tends to be very bulky and expensive. 

Formulas for passive filters: 
C are capacitors, choose high quality types, polypropylene, poly carbonate etc. -do not use electrolytics (it is a good recommendation to use several different types in parallel). 
L are inductors and shall be air core types (no metal in the cores) the copper wires shall be thick for low internal resistance.. 

12 dB filter: 
Most loudspeakers uses 12dB filters, the advantages is that the energy above the switch frequency is is minimized and the tweeter will not burn as easily if you overload the loudspeaker or the power amplifier, the down side is the phase errors produced in the inductive components which will increase the distortion.

Filter components in this table: 

6dB filter: 
The loudspeakers that uses 6dB filters often have very rugged elements and are well specified. The advantage it that the phase errors are minimized but problem may occur if you overload the power amplifier and a lot of distorted high frequent energy reaches the tweeter which may be damaged. 

Filter components in this table: