When a table has a clustered index in SQL Server does that mean that all indexed queries will go via the clustered index?
For example if I have a table with a single non-clustered index (indexing one column) and search for a row via that column it will do Index Seek -> RID -> Data row lookup -> Result
But if I add a clustered index on a different column then the same query will do the following Index Seek -> Extract clustering key -> Clustered index seek -> Results
This implies to me that the non-clustered index no longer 'terminates' with a RID at the leaf but with a clustering key of the clustered index? Is that right?
Yes, you got it pretty much figured out.
When you have a clustered index, then any non-clustered index will also include the column(s) from the clustered index as their "lookup" into the actual data.
If you search for a value in a non-clustered index, and you need to access the remaining columns of the underlying data, then SQL Server does a "bookmark lookup" (or "key lookup") from that non-clustered index into the clustered index (which contains the data itself, in the leaf-level nodes). With a clustered index, you don't need the RID's anymore - and thus you don't have to update all your index pages if a RID changes (when data gets moved from one page to another).
Bookmark lookups are rather expensive operations, so you can add additional columns to your non-clustered indices via the INCLUDE statement. With this, your non-clustered index will contain those additional columns on its leaf-level pages, and if you only need columns that are contained in that set of data, your query can be satisfied from the non-clustered index itself (in that case, it's called a "covering index") and you can save yourself a series of bookmark lookups.