Antenna design can be considered and "art" as much as a science. First you start with what "it should be like" then experiment with it until it becomes that. A Yagi can be as simple as 3 peices of wire of the correct length, spaced to suit the frequency. It can also become a complex mess of reflectors and directors that looks like some crazy pile of ladders.
A classic simple 3 element Yagi looks like this: ( brace yourself for bad ASCII art )
I
I I
I I I
I I I
I I I
I I
I
The longest element on the left is 0.55( wavelength ), the middle ( which is in two equal pieces ) is 0.5 ( wavelength), the last is 0.45 ( wavelength) . The spacing between , left to right, is one tenth of the wavelength. The small end is the direction to point the antenna.
Wavelength is calculated by : L=v/f where L = wavelength, v=speed of light ( 300,000 m/s ) , f = frequency
giving, for say 100MHz, L= 300,000/100,000 or 3 meters.
Plugging this into the above, gives us this:
0.55(3)= 1.65 meters
0.5(3)= 1.5 meters
0.45(3)= 1.35 meters
spacing = 3/10 = 0.3 meters
Of course, this will result in a fairly poor antenna, due to the limited number of elements, one reflector, on driven element, and one director.
I think you would probably find that many designs for what you need to do already exist on the internet, especially things like the "can-tenna" made from a potato chip can, used on wireless routers.
What is the antenna to be used for? Narrowing it down will help greatly in deciding what type of design would be best for your needs.