Some things I've found learning on the game and with the help of these forum members.
1) Speed is almost universally the #1 trait. The faster your players get to the ball, the better your odds (or the faster you can run away with the ball).
2) Don't play it like a simulation/real life. It's a video game and there are certain benefits. If you have a fast, agile, quick accelerating player, you can bob and weave around defenders like you can't do in real life and wouldn't think of doing if you were not aware of the possibility.
3) The standard lineups for your team are often not the best for madden play.
4) Not all plays are created equal. It seems that some plays just work better with more regularity than others. You need to find several of them and then set them up in your audibles.
5) Disguise what you're doing on O and D. The more unpredictable you can be and still do what you want, the better you can be. Especially true on defense. If you can make the defense look the same, but stop the run and pass, then you can bring guys from different positions for heat and the O will never know where it's coming from. This means learning what all the defensive shifts are and getting around your players fast to make the manual adjustments. It takes practice - a lot of it, but it pays off big.
6) Get your best personnel on the field. This may mean playing some guys out of position or coming out in a formation to get your personnel and then using an audible to pick your play.
7) The practice field is a good place to get to know your plays, routes, etc. Pick a random play from the defense and you can run your play against a variety of CPU defenses.
Play other people. It will help you get faster as you can see what other people are doing.
9) Spend some time just reading this forum and watching the videos. There is lots and lots of information here.
10) You can purchase a guide/e-book. They show you a series of plays/strategy to use that work together. While it is a sort of shortcut, it can also help you to understand more of what to do by comparing what you think vs what better players are doing.
Also, there is a link in one of these forums/sites that has all the playbooks (O & D) as well as a spreadsheet somebody did that shows the type of plays in each playbook (i.e. how many plays from the I formation or from Shotgun trips, etc.)
Have fun. While there are a lot of legitimate complaints, the game really is quite deep and is a lot of fun more times than it isn't.
Oh - also, create a fantasy team/franchise. It'll help you learn what attributes are worthwhile and which aren't.