Basically pt-tc runs checksum on all tables on the master and on each of its slave. It first runs a a checksum on the master tables, once its done with the master it will run a checksum on each slave one at a time. If there are any differences on the slave, pt-tc will modify this_cnt and this_crc columns on the slave server. After running checksums on all slaves it will print out a report on the differences/errors etc.
You can then run a query on the checksum_table to determine which tables have diverged from the master, you have to execute this query on each slave server.
It does not modify any other table except the checksum_table which is percona.checksums by default unless specified explicitly.
So you can execute pt-table-checksum at a regular basis (eg every night or once a week), and then use something like Percona Monitoring plugins to run pmp-pt-table-checksum on each slave server to report/alert if there are any slave that have drifted.
Lastly, the best way to understand the tool is by using it and/or running it with PTDEBUG=1.