How do I map an island in a lake using iD editor and the multipolygon tag

Although the "iD cannot handle relations so far" answer was 100% correct at the time, it now can (sort-of) handle multipolygon relations.

Here's what I think you need to do:

1. Add the area for the outer (the lake in your case) and tag it as a lake
2. Add the area for the inner. You don't need to add any tags here.
3. shift-select both.
4. The radial menu should have a "+" on that ("merge", keyboard shortcut C). Press that. You should have created a multipolygon.
5. Of course, save, if you are satisfied.

One that I created on the test server using this method is here:

http://api06.dev.openstreetmap.org/relation/4295222887

(it won't render because it's on the test server).

The method above does leave an "area=yes" tag on the inner which, while not wrong, is unnecessary. There may also be a better way to do it - I don't know because unfortunately there's no help in iD worthy of the name and wiki documentation is sadly lacking (I suspect most wiki editors are JOSM users). I did raise this, but the iD authors' priorities are elsewhere.

As far as I know iD cannot handle relations so far.