Having 4 kids, I seem to need several different ways to tackle this growing problem.
We try to limit how long a child can be on a device to 2 hours. The kids are used to sharing, as it's a busy household, so this rule does tend to get followed.
Of course, sometimes you don't want them on for that long. With my youngest 2, I tell them they need to spend some time outdoors before they are allowed to carry on playing. My son is particularly unhappy with this tactic, as he has autism and his current obsession is games & computers.
Another tact we try with my youngest 2 is getting them to earn time on games by helping out a little around the house. Yes, they often moan that it's not their job, or that they should get money for it, but we feel it teaches them about co-operating with the running of the household.
For my eldest 2, I do sometimes have to resort to switching off the router. This is a bit of a pain, but it is the most effective way of getting them conversing with the family.
Finally, we have rules about how we all eat our evening meal together round the table, and no one can bring phones/tablets/watch tv during this time. We also insist people stay seated at the table until everyone has finished eating. Old fashioned, I know, but it ensures that at least once a day we are all chatting to each other without anyone distractedly staring at a device.