Get CultureInfo from current visitor and setting resources based on that?

Request.UserLanguages is the property you're looking for. Just keep in mind that this array may contain arbitrary (even non-exsitent) languages as set by request headers.

UPDATE

Example:

// Get Browser languages.
var userLanguages = Request.UserLanguages;
CultureInfo ci;
if (userLanguages.Count() > 0)
{
    try
    {
        ci = new CultureInfo(userLanguages[0]);
    }
    catch(CultureNotFoundException)
    {
         ci = CultureInfo.InvariantCulture;
    }
}
else
{
    ci = CultureInfo.InvariantCulture;
}
// Here CultureInfo should already be set to either user's prefereable language
// or to InvariantCulture if user transmitted invalid culture ID

Asp.Net Core version: using RequestLocalization ie the culture is retrieved form the HTTP Request.

in Startup.cs - Configure

app.UseRequestLocalization();

Then in your Controller/Razor Page.cs

var locale = Request.HttpContext.Features.Get<IRequestCultureFeature>();
var BrowserCulture = locale.RequestCulture.UICulture.ToString();