Speed comes with experience, most of us have been doing it for years, if not decades, and a lot of it's just down to muscle memory. Watch an Experienced Postie and regardless of all the preperation Indoors once they're Outdoors they're basically on Automatic Pilot.
Whipping out a bundle of mail... slipping off the elastic bands (and putting them in their pocket)..... checking the address on top (although you're not meant to "Walk & Sort" most of us do it).... Thinking ahead to how does the gate open, where's the letterbox, is it a bastard to open, is there a snappy dog on the other side..... Getting the mail ready as you're walking up the path (which could be rolling it up like a sausage roll if they've got a stupid vertical letterbox) ... and then firing it through the letterbox in a brisk efficient manner.
If they've got a package bash the door with the PDA (and ring the bell just incase it does work) that gives the occupant time to get out of bed, the shower, off his game etc, while they rummage in their bag for the package. If they don't get an immediate response i.e "Hang on I'm in the crapper" they'll start writing out a 739( (red card) or if they're nice looking for a safe place to leave it. Then repeat a couple of hundred times for that day.
Is it any wonder that you're not going to be as FAST as an experienced Postie that you may be working with?
Years ago they used to teach that the main priority for us was "The Security of the Mail". If you're not sure of something, or can't find an address just bring it back to the office. With the shite state of the company nowadays it's no wonder everyone's trying to prioritise SPEED above all else. Ask them if it matters if you put the mail through the wrong door ... see what they say. 
. (but the days I don't work are Monday and Tuesday which are much lighter..........)