Be wary of lazy comparisons between Britain's Labour Party and the U.S. Democrats or between Jeremy Corbyn and Bernie Sanders. Let's not put too much hope in Corbyn's advance and over-emphasize its effect on things here in the United States. Let's not confuse a labor party---any kind of labor party---with the Democrats, but let's also not use that as a reason to not encourage the most progressive tendencies among the Democrats. Let's also get past the talk of Trump's pretended populism while we're at it.
What can we learn from Corbyn's advance? Trust the people, trust the young people, trust the working class, take advantage of the contradictions which our opposition creates, force the opposition to ally with unsteady political forces through organizing, it is labor party politics (and not Green or sectarian distractions) which first wins people's attention, and don't ever be afraid to support and defend public services.