Countif function between two dates

I have written the following countif formula, but need to add a second criteria and cannot get it to work.

=COUNTIF(A1:A9, ">=1/1/2008")

I would like to have an equation that can count the number of occurances between two dates (so I can count visits per quarter). For example, 1/1/08 to3/31/08. Once I get the number of visits per quarter I will multiply it by a dollar amount. However, each visit (column) has a different dollar amount associated with it and the visit windows in each column will all be at different times during the year.

The equation above is all inclusive for anything greater than 1/1/08. Any help would be appreciated. If there is a better way to do this I am open to suggestions.

I looked at the information you sent, but it still doesnt help me with a date range. I may have overlooked it though. The example below is closest to the one that would help me, but my primary focus is to count the number of cells that have a date between 01/01/08 and 3/31/08. The SUM is not the main issue for my worksheet .

Example 2: To count the number of sales in 3 locations of service since a given time period.

Solution: In it's basic elements, this is a simple test. If the date to be tested against is in a cell it would be a simple
=SUMPRODUCT((C5:C309>$A$1))*(H5:H309="A"))
But this formula shows a technique to use embedded date strings that works, as far as I am aware, in all international versions of Excel.
=SUMPRODUCT((C5:C309>(--("2004/05/31")))*(H5:H309="A"))