1. do you mean static (.a), as opposed to dynamic (.so) ?
2. does this library need to be built outside of the source tree?
For 2. i took the liberty of looking myself, and it does not.
The complete steps are (as listed in the README):
tar xf grib_api-1.0.0.tar.gz
Search LQ / Google for "how to uninstall from source", "checkinstall", "slackbuild" and/or "src2pkg" if you are concerned about removing once installed or you intend to deploy over more than one machine by building a package.