I've heard rumors about needing additional war assets to get the good ending even if I made all the right choices in my playthrough. What do I have to do to get the good ending?
In the single player you start gaining War Assets. War Assets are assigned a point value. These values are added up and shown in two ways; Total assets, and Effective assets. Total Assets are everything you have gathered. Effective assets are what can effectively be used in the final portion of the game. Effective assets are also are what determine which of several endings you can get. The higher the effective assets the better the ending.
During the multiplayer you will have noticed you have been increasing Galactic Readiness. Galactic readiness directly effects how much of the total assets become effective assets. So if you get galactic readiness too 100% then your total assets will all be effective, instead of having some assets not count. This makes it much easier to get the best ending.
Keep in mind that the multiplayer-boosted "Readiness" factor will degrade over time. So even if you boost it up to 100% now it will not remain that way until summer. I don't know what the rate of decay is, but I've heard it is about 1 or 2% per 12 hours of real-world time. So you will have to play more multiplayer towards the end of your single player run if you want that value to be at 100% for the endgame.