The main way of designing FIR filters (more accurately you are deducing the filter coefficients) is through one of two methods:
1. The Window Method
2. The Frequency Sampling Method
Both methods can be easily implemented on DSP chips, hence are used for rapid IR filter development. There are other methods for deriving FIR filter coefficients, however the above two methods are the only two I have used. I suggest a bit of Googling for the above two terms will shed some light on how the techniques work.
First you need to determine the type of filter, such as Low Pass, High Pass etc. Then, you want to determine the specifications of the filter such as stop band and pass band edge frequencies, stop band attenuation and the sampling frequency.
You also need to figure out which window function (if using this method) is best for these specifications. Another factor that determines the type of window that you will use is the number of terms of the filter. The more terms, the more memory that you will use up, but will gain more accuracy in certain cases.
Using a LP filter as an example, you would take your window function and corresponding Ideal Low Pass Impulse Response function (which would be in the form of a Sinc function) and multipy term by term. The you want to shift the resulting impulse response to the right for causality to start at an index of 0 all the way to N -1 ( N being the number of terms of the filter).
This is a "rough" description of FIR filter design. Of course, there are some details that were left out, but a good DSP book would go into alot more depth in this topic.