I have never trusted Tepco or anything they say.
Let's just say it involves jars and is not very pleasant. The jars' contents are then analyzed by gamma spectroscopy primarily, although I would expect they would also be doing alpha monitoring as well since reactor fuel could possibly have been taken internally.
The reason it takes so long is because of the biological half life, i.e. the time it takes the body to eliminate half of the radioactive elements through normal bodily functions.
Quite a contrast to 134 Chernobyl workers in the first few hours recieving 800m/Sv-16000m/sv.
If that is all of the over exposure, so far, it is a testament to the overall plant design. We just lost 300 or so people in one weather event, and Japan lost something north of 20K in the earthquake/tsunami, that had nothing to do with nuclear power.
“Internal” exposure is exposure from radioactives inhaled/ingested/absorbed through the skin.
Measuring internal dose is done by a number of methods, including measuring the radioactivity of waste matter, blood, perspiration, etc. You can also use a whole-body counter to measure gamma ray activity inside the body.
Why did it take a month? They may have been too busy dealing with the reactors to stop and hang around inside a whole-body counter. Or, perhaps they wanted to evaluate how long the radioactives were hanging around in the body, the better to get an integrated dose.