Hi, noiz and rbobbitt!
Awk command that will display the total number of fields in a file, can be like this:
awk '{ sum += NF } END { print sum }' inputfile
Because awk's variables (other than built-ins) are initialized to the null string, by default. This null string has also numerical value zero. So, you can skip BEGIN section. I like this feature of awk and other scripting languages.
KP.