Let us consider three replicates, and at each replicate we have two large fields. A diagram of this would look like this:
We will randomly assign the low (-1) or high (+1) level of factor A to each of the two fields. In our example A = +1 is irrigation, and A = -1 is no irrigation. We will randomly assign the levels of A to the two fields in each replicate. Then the experiment layout would look like this for one replicate:
Similar to the previous example, we would then assigned the treatment combinations of factors B and C to the four experimental units in each block. We could call these experimental units plots -- or using the language of split plot designs -- the blocks are whole plots and the subplots are split plots.
The analysis of variance is similar to what we saw in the example above except we now have A rather than ABC confounded with blocks.
See the Minitab project file 2-K-Split-Plota.mpx as an example. In addition, here is a viewlet that will walk you through this example using Minitab v.16.