Which specific fields in a database should be indexed to speed up the execution of a certain query?

Index the fields that are involved in filtering conditions (WHERE), sorting (ORDER BY), joins (JOIN), and grouping (GROUP BY) in queries, especially if these fields are frequently used and the table is large.

For example, if there is a query:

SELECT * FROM orders WHERE customer_id = ? ORDER BY order_date;

it makes sense to index the customer_id and order_date fields.

It is important not to index too many fields unnecessarily, as indexes occupy space and slow down insert and update operations.

Also, consider the types of indexes (e.g., B-tree, hash) and composite indexes if the query filters on multiple fields simultaneously.