Is LINQ Join operator using Nested Loop, Merge, or HashSet Joins?

First it effectively creates a lookup from the "inner" sequence, then iterates through the outer sequence. It can then look up each key from the outer sequence and yield each appropriate pair. Something like this (ignoring argument validation etc):

public static IEnumerable<TResult> Join<TOuter, TInner, TKey, TResult>
    (this IEnumerable<TOuter> outer,
     IEnumerable<TInner> inner,
     Func<TOuter, TKey> outerKeySelector,
     Func<TInner, TKey> innerKeySelector,
     Func<TOuter, TInner, TResult> resultSelector)
{
    Lookup<TKey, TInner> lookup = inner.ToLookup(innerKeySelector);
    foreach (TOuter outerItem in outer)
    {
        TKey key = outerKeySelector(outerItem);
        foreach (TInner innerItem in lookup[key])
        {
            yield return resultSelector(outerItem, innerItem);
        }
    }
}

The lookup will use a hash table internally for the keys, so that it's efficient to look up any individual key.