How to run a bash script from a Makefile?

Just like calling any other command from a makefile:

target: prerequisites
    shell_script arg1 arg2 arg3

Regarding your further explanation:

.PHONY: do_script

do_script: 
    shell_script arg1 arg2 arg3

prerequisites: do_script

target: prerequisites 

Perhaps not the "right" way to do it like the answers already provided, but I came across this question because I wanted my makefile to run a script I wrote to generate a header file that would provide the version for a whole package of software. I have quite a bit of targets in this package, and didn't want to add a brand new prerequisite to them all. Putting this towards the beginning of my makefile worked for me

$(shell ./genVer.sh)

which tells make to simply run a shell command. ./genVer.sh is the path (same directory as the makefile) and name of my script to run. This runs no matter which target I specify (including clean, which is the downside, but ultimately not a huge deal to me).