Are there any industry standards for PRFs? I mean something like a NIST, ISO, FIPS or similar standard which defines a constructions for a PRF.
HMAC is the standard way to construct a PRF from a hash function.


FIPS PUB 198-1 - The Keyed-Hash Message Authentication Code (HMAC) (NIST standard)
RFC-2104 HMAC: Keyed-Hashing for Message Authentication (informational RFC)
ISO/IEC 9797-2:2011


(Unfortunately the above standards only describe it as a MAC, not as a PRF)

It's also very popular in practice. For example it's used in SSL/TLS, SSH, HOTP/TOTP.

I recommend using it with SHA-2 as the underlying hash function. Though technically the known weaknesses of MD5 and SHA1 don't apply to keyed use in HMAC, so even those obsolete hashes could still be used as PRF in the HMAC construction.