The first thing to remember is that filing amendments is not something obligatory according to the law. This is because the IRS will probably send you the revised bill based on Form 1099 or K-1 when they process your return. Even if something happens after filing that make your return inaccurate, you do not have to file an amendment. The thing to consider when contemplating filing an amendment is whether all the details you reported at the time you filed your tax return were true and accurate. If so, you do not need to file an amendment.
On the other hand, if you knew that details in your tax return were not true or accurate when you filed it, you should file an amendment before the IRS discovers it. It would be rare for the IRS to bring up your filed tax return in an audit or criminal prosecution once you have corrected it by filing an amended return.
Another thing to bear in mind is that if you file an amended return, you cannot pick and choose what to declare in your amendment. You cannot only amend details that will gain you a higher tax refund, for example, and neglect declaring other details that may increase your tax liability. Amending a tax return means correcting all inaccurate details.
That said, there are some inaccuracies that do not warrant an amendment such as calculation errors, omission of a Form W-2, schedules etc. This is because the IRS corrects calculation errors for you and can process your return even without these types of documents. If any further details are required, the IRS will ask for them.
Also bear in mind that there are some details that cannot be amended. For example you cannot change your status from married filing jointly to married filing separately after the deadline for submissions have passed (April 15 each year).
Filing an amendment is done through filing Form 1040X Amended US Individual Tax Return. Remember the time limit you have to make an amendment is either 3 years from the due date of your original filing or 2 years after paying your taxes, whichever is later. If you are amending to receive an additional tax refund, it is better to submit your amendment after receiving any tax refund due on your original submission.
Finally, filing an amended tax return cannot be done electronically; it has to be done on paper.