The general approach I use with ND filtration is to compose and meter your scene first without filtration. I also use the Lee filter holder, which has the handy feature that allows you to clip/unglip the actual filter holder to/from the lens adapter fairly easily. The general process to expose for any amount of ND filtration, including the Big Stopper or other large-stop filter, would be as follows:

1. Attach the Lee filter adapter ring to lens. Set camera to Manual mode.
2. Fully meter the scene at a fixed ISO of 100:
   • Evaluative metering will work well with average scenes of relatively balanced tonal range. (Make note of shutter speed.)
   • Selective spot or partial metering will often be necessary with scenes of divided contrast or uneven tonal range. (Make note of shutter speed.)
   • If you are also using Graduated ND to compensate for contrast, meter highlight, midtone, and shadow areas to determine total dynamic range
     • Set aside the shutter speeds for graduated compensation in a later step.
3. Compose scene in-camera without filtration.
   • Adjust aperture here if necessary for artistic/stylistic effect.
4. Apply ND filtration and compensate shutter speed:
   • Multiply the shutter speed by the filtration factor:
     • This is easy to calculate. Take 2 to the power of the number of stops of ND filtration:
     • If applying a 2-stop/0.6 ND filter, multiply shutter speed by 22, or 4
     • If applying a 10-stop/3.0 ND filter, multiply shutter speed by 210, or 1024
5. Apply Graduated ND (GND) filtration (Optional):
   • GND filtration should not be compensated for in-camera, as the intent is to mitigate highlights for a given exposure.
   • The amount of GND filtration necessary in stops can be computed as follows:
     • Divide the longer shutter by the shorter shutter.
     • Take the log of the shutter speed quotient
     • Divide the first log by log(2)
6. Apply white balance correction (Optional):
   • If you are using a considerable amount of ND filtration, strong color casts may appear
   • These can be corrected in post, however they are often EXTREME, and may not be fully correctable
   • To ensure viable correction in post, compensate in-camera first (according to manufacturer's recommendations and settings)
     • Lee BigStopper tends to cast very, very blue...so set WB to around 10k or more
     • HiTech 10x ND also tends to cast rather blue, so a setting near or even above 10k might still be needed
     • Other brands may cast very magenta or violet-blue, some cast very green or yellowish

If you have a smartphone with a calculator, computing these is extremely easy in the field. You can also try to memorize a few things to help you quickly arrive at rough settings without the need to use a calculator. Here is a table of ND stops filtered to shutter speed multipliers (Ratios provided for Lee/Singh-Ray filter users...just add up all the fractions of your ND filter stack):

 ND Stops | ND Ratio | Multiplier
==================================
     x1   |    0.3   |       2
     x2   |    0.6   |       4
     x3   |    0.9   |       8
     x4   |    1.2   |      16
     x5   |    1.5   |      32
     x6   |    1.8   |      64
     x7   |    2.1   |     128
     x8   |    2.4   |     256
     x9   |    2.7   |     512
     x10  |    3.0   |    1024
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Example Scenario #1: Simple ND filtering

You wish to photograph a serene river scene, completely blurring out not only the motion of water, but also the slight rustling of the leaves of the trees, creating a very dreamy style of photograph:

• The scene has roughly even tone, no GND filtration is needed
• You use evaluative metering, and compensate down by 1/3rd of a stop
  • Aperture f/8
  • ISO 100
  • Shutter meters at 2 seconds
• You want to apply 6-stops of ND filtration (1.8 ratio)
  • Shutter speed needs to be increased by a factor of 64: 128 seconds, or about 2 minutes

Example Scenario #2: Complex ND+GND layered filtering

You wish to photograph a cloudy coastline just after sunset, blurring the soft waves to a fog and flattening clouds. You need to compensate for the sun, which is just below the horizon and brightly illuminating the sky relative to the sea.

• The scene has high contrast, so GND filtration is necessary
  • You spot-meter the sky near the sun, and get an exposure of 1/50th second
  • You spot-meter the sea near the horizon, and get an exposure of 1/3rd second
  • You spot-meter the rocky coastline, and get an exposure of 1 seconds
  • Total difference in stops between the sea and sky: @4 stops
    • log(1/3rd / 1/50th) / log(2) =
    • log(.3333 / .02) / log(2) =
    • log(16.6667) / log(2)
  • Total difference in stops between the sea and coast: @1 2/3 stops
    • log(1s / 1/3rd) / log(2) =
    • log(1 / .3333) / log(2) =
    • log(3) / log(2)
  • (Check) Total difference in stops between sky and coast: @5 2/3 stops
    • log(1s / 1/50th) / log(2) =
    • log(1 / .02) / log(2) =
    • log(50) / log(2)
  • Three levels of GND filtration necessary:
    • One 2-stop soft grad filter for the division between coast and sea
    • One 3-stop and one 1-stop hard grad filter for the division between sea and sky
    • Alternatively, drop the extra 1-stop hard grad if you are worried the sky may end up too dark with an additional 10-stop filter, or you intend to slightly under-expose to preserve highlights
• You use center-weighted or partial metering on the sea:
  • Aperture f/8
  • ISO 100
  • Shutter meters at 1/4th
• You want to apply a 10-stop BigStopper (3.0 ratio) or similar ND filter
  • Shutter speed needs to be increased by a factor of 1024:
    • 1/4s x 1024 / 60s/m =
    • 0.25s x 1024 / 60s/m =
    • 256s / 60 s/m =
    • 256 second or 4m 16s exposure time