If a satellite is to be inserted into a retrograde orbit (opposite to Earth rotation direction) is it accelerated straight in the desired "westwards" direction until (after overcoming Earth rotation speed) orbital speed is attained, or is it first inserted into a prograde orbit and then some engines of lower thrust but better specific impulse are used to gradually turn its orbit, through polar, into retrograde - or maybe is some other trick used?
For retrograde launches, the launch azimuth is westwards from the beginning. It would not be viable to first go into prograde orbit and then change the inclination into retrograde trajectory. Such huge inclination change would require an awful amount of fuel, because effectively it would be like killing the speed in the prograde direction (over 7 km/s) and gaining the same speed in the opposite direction.
A common example of a launcher that always launches retrograde, is Israel's Shavit booster. Due to the nature of its neighbours to the east, and the fact most space launches closely resemble ICBM style launches (which might cause some concern on launch) and no where safe to drop empty stages, they launch west over the Mediterranean Sea.
For more on that see answer(s) to The strange orbit of Ofeq 11 - how does it (actually) do this?