Make sure you have all the desired players from that league on your team before the last game (championship). You will not be able to get the players if you win the championship because you will move on to the next league.
While creating a Superstar custom character, assign his awareness attribute to 0. Doing so leaves you with more points to assign to other desired attributes. Once done, go to the IQ test and fail it by letting time expire. You'll receive a notification that you did poorly, which adjusts your awareness rating from 0 to 99.
Start a franchise with the trade deadline off, then sim or play the season to Week 17. Find out which team has the worst record. Trade your first draft pick for their first pick and they will always accept. Note: You can also do this with second through seventh draft picks as well.
To keep a good player under the salary cap for a long time, when signing players, sign them for seven years. Give them nothing for a signing bonus. Give them the minimum they will accept for the seven year contract. Your player will then have a seven year contract with the same salary for those seven years. The salary cap will go up each year but their salary will remain the same, so you will actually have more room under the cap for your other players over the following years. When drafting a rookie, also sign him for seven years. Give him $70,000 for bonus and give him the minimum for the contract. This way you will also save on the rookies for a long time. Sometimes your players will holdout but it is worth it in the long run. If you get fed up with your highly paid player or get a better one cheaper, you will be charged nothing in penalty the following season.