performance - Performing bounding box query in PostGIS?

I have a PostgreSQL table, with almost 2 million rows, with a long-lat coordinates field in the form POINT(-73.4938 33.2405).

Supposing there's a geospatial index on that field, what's the most efficient, fastest way to select all the rows within an arbitrary bounding box?

The box is like SW long-lat: -74.0042 40.7688, NE long-lat: -73.8809 40.7984.

Answer

Assuming the given bounding box limits are in the same spatial reference system as the stored coordinates, and you know which spatial operator (intersects or contained by) you need:

SELECT *
FROM   my_table
WHERE  coordinates 
    && -- intersects,  gets more rows  -- CHOOSE ONLY THE
    @ -- contained by, gets fewer rows -- ONE YOU NEED!
    ST_MakeEnvelope (
        xmin, ymin, -- bounding 
        xmax, ymax, -- box limits
        my_srid)

Alternatively, if you prefer the sound of "contains" (instead of "contained by") the WHERE clause should be flipped:

WHERE  ST_MakeEnvelope (...)
    ~ -- contains, gets same fewer rows 
    coordinates 

PS: Given (by OP after the above was posted) that the records are simple points, I think that the difference between "intersects" and "containment" becomes very subtle, affecting only the points on the edges of the bounding box.