This video gives a great overview of how the string instruments are tuned effectively, but please also look at my points below.
Store instruments in a place that is not too hot or cold to reduce the amount of tuning you will have to do!
Strings will break if overtightened, and can snap into a child's face or body. I recommend that, at least at first, only adults should use the pegs. Once strings are close to the correct pitch, the fine tuners can be used by students to get an accurate pitch.
Tuning by ear (as they show in the video) is a great skill that we work towards! If you are tuning by ear, this website is great for getting good sounds of the open strings.
Few students (or adults!) are able to tune by ear yet, so tuners are a great option. In school we use Snark Clip-on Tuners, which are a great inexpensive option if you want to purchase one and leave it in your instrument case.
If you don't have a tuner at home that can "hear" the violin and give feedback, there are tuners online! This one works great.
It is recommended to always start below the pitch the string should be and carefully work up using the pegs, pushing in and turning slowly at the same time.
If something goes wrong (a string snaps, the bridge falls, etc.) please defer to a professional. Unless you have training in instrument repair, be careful about fixing something yourself. You may accidentally cause further damage.