If you found issues with .NET Core you can use GitHub to let us know, using the following repos:
If you found issues with .NET Framework, please submit your issues through Visual Studio and .NET Framework Connect website.
If you need help there are a lot of ways you can connect with the team and seek out assistance.
StackOverflow is one of the most used sites for asking general purpose programming questions, and no wonder there is already a number of existing questions tagged with coreclr as well as questions about Roslyn.
Call us old school, but we do love to write detailed content for people to consume, and our blogs are the main outlet where you can find this content.
@dotnet on Twitter is the main Twitter account you can follow to keep in touch with the team and get updates.
Of course, do not miss out on these other teams that are closely related to .NET Core.
.NET Foundation keeps an active public forum (BBS-like) that you can find on .NET Foundation Forums.
Gitter is IRC for GitHub projects. There are always people there ready to help with various questions around .NET Core, CoreFX and Roslyn.
Here is a list of events for the set of .NET user group meetups from meetup.com.