The whole package is a big thing to swallow at one brain gulp. I recommend getting the sample datasets and playing with them a little with the interactive program, while reading the manual. Then figure out how to put your own data into the AFNI dataset format, and away you go!
There are two types of datasets: Anatomical and Functional. Data direct from the scanner is Anatomical. Functional datasets are derived values designed to show where brain function is happening. Therefore, you almost always use to3d to create anatomical datasets. However, it is possible to create functional images outside of the AFNI package in some way (your own custom code, perhaps) and then assemble those images into a functional dataset for viewing with the interactive AFNI program.
Datasets can be "3D" or "3D+time". The latter consists of 2 or more 3D volumes of voxel data that are to be considered as having been gathered in temporal sequence. In the AFNI program, 3D+time datasets can not only be displayed as images, but can be graphed vs. time. More germanely, a 3D+time dataset can be processed using the "correlation method" to produce a functional dataset - that is, a 3D dataset that when properly displayed is a brain activation map.
The sample 3D+time dataset, in the file sample96.tgz is a good place to start. You can use to3d on it, and also use it to play with the AFNI display and analysis tools. Information about how to read your particular (not to say peculiar) 2D or 3D image format can be found on the AFNI FAQ List.
At MCW, we refer to the results of the correlation method as "FIMs", named after the first program that implemented this algorithm (FIM=Functional IMage?). In AFNI, a FIM is computed from a 3D+time dataset via controls present on the Graphing window. The procedure is explained in the main manual for AFNI.
You may want to register (align) your images before functional activation analysis. This can be done using the program 3dvolreg, which takes one 3D+time dataset as input, and produces a new one as output (hopefully a better one). At present, the only documentation for this program is the output of "3dvolreg -help". (Most programs in this package take the command line option "-help", which will print out a terse summary of the program's usage. This is the AFNI package analog of man pages.)
The grid for displaying images is always controlled by the current anatomical dataset being shown in AFNI. If needed, the functional dataset will be resampled (interpolated) to the anatomical grid before being used to compute the overlay colors. This process can be controlled by the "Define Datamode" control panel on the main AFNI control window. The correlation threshold and functional-intensity-to-color mapping are controlled from the "Define Function" control panel. To actually see the color overlay for a functional dataset, the "See Function" toggle must also be turned on.