If a host has a LOC record, it can be looked up via dig -t loc:
$ dig +short -t loc geoffstratton.com 32 47 32.599 N 96 48 53.11 W 125m 10m 100m 10m
LOC records are expressed in terms of Degrees-Minutes-Seconds, not decimal latitude and longitude. You can convert them using a tool like the FCC’s latitude and longitude converter.
Publishing a LOC record is pretty simple: just go into your DNS service add an LOC record type for your domain name alongside your usual A, CNAME, and MX records. You’d probably be using BIND on Linux or Windows DNS.