I had exactly the same issue when starting out with a base application using Entity Framework 6 for the first time.
The best solution for me was to ensure only one DbContext instance during the request life cycle using Autofac (with MVC integration) and Autofac's InstancePerRequest lifetime scope.
If you're interested in going down the dependency injection route (which I'd strongly advise) I would recommend familiarizing yourself with Autofac - and for more information on your particular issue check out davidbitton's answer here - it will get you on the right track.