Not an instructor, but I can tell you how we do it in the airline I'm in, we are doing the same approach in the jets as when I go fly a Seneca. Well OK, maybe a tad faster.
Basically you don't need to remember anything except work from the top down. We use Aerads.
So, first, set up everything you'll need (Navs, Coms, etc.) and think it through in your head before opening mouth.
This includes thinking about the weather - if its a stonking cross wind it maybe worth mentioning, or if there is very low cloud.
Obviously STAR may come into it, but just talking about the approach here, you want to go first through the plate starting at the top and basically saying everything on the plate, starting with the plate "code". So... ""the approach is on plate "M1", the ILS/DME approach for runway 03. The transition level is XXX, the MSA is XXX. Then any relevant notes, such as about speed or offset approach. Then we are onto the bottom of the plate, the plan view, reading from left to right. Something like "overhead the XXX VOR, at 5000 feet, outbound on the 234 radial, descending to a platform height of 2500 feet, left turn, inbound course is 031 degrees, final approach fix is at 5.5 dme based on the I-MEY and its a 3 degree glideslope.
The minima I will be using is 200 feet/ 550 metres.
Should I need to go around, I will go full power, raise the nose and when happy that we are climbing I will raise the gear (and flaps on schedule).
The missed approach point is at the threshold. (Then basically read missed approach. Correctly!). Then brief the runway itself. With a bit of practice you can get a really good flow going. So ... top to bottom, the left to right, then missed approach.
Don't forget to talk about speeds and don't forget to check any notes at the beginning regarding special procedures such as speed restrictions, etc.
Hope you don't mind me butting into the Flying Instructors Forum......