How are METARs published?
METAR

The METAR always refers to a specific airport and is obtained right then and there. That is at the airport.

It is a report of current conditions, usually hourly.

In the US, the FAA polls all systems remotely and disseminates the reports in METAR format. No word on wether this is via phone, mobile or radio, if that is what you are asking. 

In Germany, the DWD, the german weather service, provides the reports. It can be assumed, that the situation is similar and that the stations are polled.

Weather stations have wide-ranging capabilities and operators, so the reported parameters may be different.

METAR reports may be reviewed by an individual before being transmitted, but the vast majority are reported automatically.

METAR reports are used for aviation weather, by definition, as a "Meteorological Terminal Area Report".

TAF

The TAF is a forecast. It is updated only 4 times a day and is provided by a human forecaster on the ground. Most larger airports have a meteorologist.

FORMAT

Both METAR and TAF use similar format, but each contains elements distinct from the other.  For example, a TAF may contain a FM (from) or BECMG (becoming), but a METAR never will.

DATA SOURCES

You can use https://www.checkwx.com/ to check both.
Or http://tgftp.nws.noaa.gov/weather/current/ if you want the raw data.