Newbie Question: How to add island inside lake?

I guess the question is more about multipolygons (i.e. how to create an object as a "hole" inside another object). The existing lake should became the outer ring, and the new island the inner ring, of a new multipolygon relation. How to create a multipolygon relation depends on the editor you use, the wiki contains an illustrated example with Potlatch: https://wiki.openstreetmap.org/wiki/Multipolygon

I didn't see the steps explicitly set out in the other answers, so in case it's helpful here goes:

In iD:

1. Select the outer boundary way
2. Expand All relations, then click the plus to add a relation
   
3. Click New relation, then select Multipolygon
4. Add any tags to the multipolygon relation (name, natural=water, etc)
5. Select the outer boundary way again (which will shift you from editing the relation to editing the way), and under All relations, click where it says Role and enter "outer"
6. Create way for the island
7. Pick any tag (ie water, area, etc) in the Select feature type screen so you can get to the Edit feature screen--you can delete whatever tags it automatically added if you want
8. With the island way still selected, open All relations, click the plus, select the Multipolygon relation you just created, and where it says Role enter "inner"

In Potlatch 2:

1. Select the outer boundary way, at the bottom of the sidebar, click Advanced
2. In the Relation section at the bottom click Add to
3. In the pop up screen, click New relation
4. In the dropdown select Advanced > Multipolygon (or just shift to the Advanced tab and enter type=multipolygon)
5. Add any other tags to the multipolygon
6. Close the pop up, and add "outer" as role
7. Create the island way
8. Click Add to again and select the Multipolygon you just created, and add "inner" as role

One Potlatch 2 tip if you do a lot of relation editing there: you can repeat relations from the previously selected way with Shift-R

For help with Id look here https://help.openstreetmap.org/questions/22542/how-do-i-map-an-island-in-a-lake-using-id-editor-and-the-multipolygon-tag For Potlatch2 see Richards answer here, he made P2 and should know https://help.openstreetmap.org/questions/14732/using-inner-and-outer-relations

Hello! Have you read Tag:place=island?