Finding polygons within polygon using ArcGIS Desktop?

I am new to GIS and ArcGIS.

I have a set of polygons, some of which enclose other polygons. They are lake polygons, and within lake polygons, are smaller island polygons.

If I have a given lake polygon, how can I select or get a list of enclosed island polygons?

Also, some islands may contain lakes within the island. I would like to select those as well.

Answer

I'm assuming the lake polygons are in the same feature class as the island polygons? Also, I'm assuming ArcGIS 10, but the below method will work in 9.3 etc. also.

But the simplest way of doing this, assuming that you don't need to know which island/lake is contained by which other lake (ie, just a selection of islands in lakes) then in the table of contents for ArcGIS duplicate the layer (add it to the ArcMap session twice) and rename one so they have different names.

The from the first feature class (I'll call it 'A') select all lake features as an attribute selection. This can be done with Select by Attributes from the Selection menu.

Then from the Selection menu choose Select by Location. We want to select features from 'B', so check that in the box up the top. In the drop down choose 'A' as the selection feature and make sure that 'Use Select Features' is checked. The from the selection type choose select within and you should be done.