For the smaller concrete works, use manual compacting such as rodding with the help of a steel rod or tamping with a wooden cross beam.
The mechanical compacting is done with the help of vibrators. This can make the compaction more effective.
Generally, needle vibrators are used for the structures like footings, beams and columns.
Take care that the shaft pipe of the vibrator should not bend too much as it can break the pipe.
Be sure to clean the needle and shaft pipe after work.