If you disconnect your negative battery terminal, you remove the power from the systems in the car. That is the first way to ensure safety for both the person working and the electrical system in the car.
There is a number of systems that will need to be activated to cause the airbag(s) to deploy. Generally short of physically powering the airbag unit directly an airbag will not go off spontaneously ( I say "generally" only because there is that one story about that one time one bag went off unprevoked, lol).
There needs to be a few modes the car must checkmark in order for the system to be ready to activate. These can include speeds above a threshold, rate of acceleration/deceleration, some cars also will read attitude/angle (such as roll over). There are failsafes, such as deployment sensors where 2 or more sensors need to be tripped for the bags to be deployed.
I wouldn't be afraid to work on the car provided you keep to working on the system you are intending to, and if it looks weird, just ask.
...Oh, and dont touch the big red button...thats an airbag deployment test button!

