Most cameras today can't detect proper exposure through the ND filter so the process to take a photo with a ND filter is (Nikon camera example):
1. Switch to M mode (or S)
2. Find proper exposure without the filter
3. Put the filter on
4. Dial shutter speed to the value ND Filter tells you
5. Take a shot!
The formula we use to calculate the values is Tnd = T0 * 2^nd, where Tnd is shutter speed with the filter, T0 is shutter speed without the filter and nd is filter density (1, 2, 3, ... 13).
Code for the app is available at https://github.com/nciric/NDFilter.