How can I access the browsers localStorage in Blazor?

It might be implemented by default into Blazor but for now I'm using: Nuget - BlazorStorage

For 0.1 you need to write your own javascript interop. But I believe this is something worked on, and maybe in the 0.2 release.

Alternatively (if you don't need storage between sessions) you can write your own DI singleton, like done here: https://github.com/aspnet/samples/blob/master/samples/aspnetcore/blazor/FlightFinder/FlightFinder.Client/Services/AppState.cs

Edit
There is an open PR for this, so indeed should be there soon: https://github.com/aspnet/Blazor/pull/205

Edit2 0.2 is done, but no localstorage yet. In the meantime i've developed a package for this: BlazorExtensions also on nuget