Of course the usual "know your flows and callouts" forward and backward. I still know the after-landing FO flow by heart after being a captain for awhile. When I get in the airplane after another crew brings it in and I see things like transponder still on TA/RA and such, I know the FO missed it twice, first on their flow and second on the checklist.
Don't do a brain-dump after groundschool. Aircraft systems knowledge is important for the line too. I've seen a crews do some really dumb things because of a lack of systems knowledge.
Think ahead. Don't be lazy. Remember you're a required crewmember, not a lemming. Teamwork is the idea.
When you get to sim training, keep up with tuning radio frequencies and such. Figure out what you'll need for clearance delivery, ramp, ground, tower, departure, etc. Many sim instructors won't pay attention and will let you get away with slop. It will make IOE and flying the line easier if you know how to quickly find the correct frequencies and set up the radios. Most people use the strategy of radio #1 for movement, radio #2 for ATIS, CD, operations, etc.
On the line, prepare and keep ahead of things. Starting with preflight, as an FO I began reviewing the dispatch release and charts in the hotel van, keeping in mind the CA has their job and you have your job. At most airlines it's the FOs job to get the clearance, set up takeoff performance, etc. Which runway will you probably use? What is the takeoff thrust rating and flap configuration for that runway? Will it be an icing takeoff? Any NOTAMS? Are you at some Podunk airport and will have to call FSS or Center to get a clearance? Speaking of which, write your clearances down legibly and don't take shortcuts. Yes, abbreviations are okay, but don't skip it entirely. So what if you always get 3,000 feet after departure, what about the one day it's different, then what? (There was recently a GoJet crew that got busted departing ROA for departing on course instead of flying the heading which was given to them by clearance delivery, not tower. Don't be the FO that gets your Captain in trouble because you didn't do your job.)
If the plane is there start your walk-around as soon as you get to the gate. Don't wait for the CA and FA to go get their coffee and do whatever first. If the plane was just arriving, I'd ask the gate agent to go down when they go down to drive the jetbridge instead of waiting in the terminal. The first exterior inspection of the day will take a bit longer, and you will have more work to do than the other crew members, so get a head start.
If you get there before the captain and see something obvious, like the batteries are dead and you need a GPU but the station doesn't have it hooked up, get a jump on it.
Stay in your lane, especially starting out. Don't perform CA flow tasks just to be nice, even something minor like setting the flight number, as it can be confusing and/or the CA might start forgetting to do that thing and it will be a problem on their next trip.
Write down taxi instructions for the CA. This is usually done on the FMS scratchpad. When I first started, I couldn't press the buttons fast enough, so I wrote the taxi instructions on paper, then put them in the scratchpad.
Don't be afraid to voice any concerns to the captain. "Do you think we should start the other engine now?" Captain will say "Oh yeah I almost forgot, go ahead" or "not yet, I think we will be here awhile."
That's all just on the ground, before you even get in the air. What then? Again, think ahead. But not blindly. I once had a PM get ATIS and start setting up the expected approach 600 or 700 miles away. The weather information will be stale by the time we'd get there. On the flip side, we have a few routes in our system that are like 100 miles or so. I get the ATIS and start running the landing numbers as soon as the climb checklist is complete.
Automation management and hand flying skills are important. When you're PF, work on both of these skills. Scan your instruments just like you were taught when you were in instrument training. The flight director makes your scan easier, but it's not a wholesale replacement for a scan.
Always remember the 3:1 rule. At 30,000, you want to start descending 90 miles out. You can push 80, or maybe 75, but then you're going to need speedbrakes. Have a buffer for descending through 10,000 (in other words, I'd probably give myself more than 33 miles to descend 11,000 if I'm doing VMO/MMO). Don't needlessly descend super early either. "Descend to XX pilot's discretion" doesn't mean "descend now." Use your situational awareness. If you're doing a straight in you'll probably want to be a bit lower, if you have to go to the far end of the field and turn around for an approach, you can afford to be on the higher side. When you're PF, do what you have to do. A few times ATC left us unbelievably high, I put flaps and speedbrakes out at 8,000, then a short while later put the gear down. No go-around needed. Again, the recurring theme here is think ahead.
Don't be lazy. It's tune and identify. Not tune and listen if there are beeps or not. BTW identifying the DME is not identifying the localizer, they are different systems and don't even use the same frequency.
The real airplane doesn't land like the sim. Observe how your captains land and find a technique that works for you. My landings were basically guesswork until I had about 50 hours and noticed one captain seemed to always start the flare just prior to the 500' marks going under the nose. I don't know if he was doing that on purpose or by coincidence, but I replicated the technique and it worked. (This is just an example, don't replicate this technique exactly just because it works for me in the plane I fly. No idea what plane you're flying.) Keep in mind energy management. Did you get slow on approach or cross the threshold at 30 feet instead of 35? Keep your power in longer.
After parking, get the post-flight done. Ask the other crewmembers who wants to call the hotel first. Sometimes no one will, because they thought somebody else would do it. You don't want to stand on a curb for 30 minutes after a long day.