An interesting problem! The solution will have many applications.
If the high state of the output from the "breath taken" sensor lasts long enough that you could see an LED wink, and if all you want is a display of the current respiration rate, then this is very, very do-able.
If the high state isn't that long, it is still do-able- just put a pulse stretcher on the output. (Little bit of hardware).
What makes this project easy is that the events you want to count, in computer terms, happen only once in a "long" time.
You may need to take care not to "double count" a single inspiration.
You will almost certainly want to incorporate some system of averaging the time between inspiration over a number of recent inspirations, with older ones counting for less.
For your output device, have a look at....http://www.arunet.co.uk/tkboyd/ec/ec1led4x7ser.htm
Not really relevant to solving the problem you came to the forum with, but out of curiosity, what is your sensor? Hobbyist grade, or a $2,000 device from Stryker?