"man resolver" just gets me the documentation of how to use
/etc/resolver.conf - what I'm looking for is some documentation of an
API to resolve DNS names, including A, MX, PTR and SRV records from a C
application we're developing. I've read about Bind's resolver library
and was hoping to use that.

e.g.
- Our application links to bind resolver library to process DNS calls
- The bind library contacts the local lwresd, which gets the info from
the DNS (our nameservers, which run Bind 9.5)
- The bind library passes the result back to the application

You might consider using the NLnet Labs lib dns library. See
http://nlnetlabs.nl/projects/ldns/ for details.

jaap

Disclaimer: I do work for NLnet Labs.