I have a SQL statement (that I can’t post here). When I look at its execution plan I see most of the time is sitting in sorts, followed by index scans.
Is there anything I can do to lessen the time spend on sorts? an index of any kind? Anything I can do to lessen the time spent in index scans?

Clustered index scan is essentially a table scan, where every row in the table is being examined.
You’re probably missing an index on that table for this query… look at the fields that you’re filtering by / joining on, and add indexes to these columns.
These indexes will also likely prevent the nested loop / sort operations as well.