Unlike in Canada, there was actually a procedure in place for the most recent flag changeover. It was outlined in Executive Order 10834. The relevant part is in Section 25:

"Subject to such limited exceptions as the Secretary of Defense in respect of the Department of Defense, and the Administrator of General Services in respect of executive agencies other than the Department of Defense, may approve, all national flags and union jacks now in the possession of executive agencies, or hereafter acquired by executive agencies under contracts awarded prior to the date of this order, including those so possessed or so acquired by the General Services Administration for distribution to other agencies, shall be utilized until unserviceable."

In other words the old 48 and 49-star flags were used until they wore out, at which point they were destroyed in a dignified manner in accordance with the U.S. Flag Code and replaced by a 50-star one. The government also issued a statement saying it was appropriate for citizens to do the same.

In the past, Americans often updated their old flags by sewing new stars right onto them. Some flags were made with a bit of extra blank space for just this purpose. There are some great examples of modified flags here.

There was no official arrangement for the stars on the flag until 1912, so that kind of modification was much more common before then. Nowadays flag manufacturers tend to follow or at least come close to the government specifications ("G-Spec"), so everyone's flag pretty much looks the same.

I'm no historian but have do enjoy reading up online about flag-related topics from time to time. Going along with what dream_face posted, I found this regarding displaying flags that are not the 50-star current version:

Official United States flags are always considered living, active flags. From the Betsy Ross flag to the present 50-star flag, any flag that at some time was the official flag is still considered a living flag to be accorded all due respect.

This is quoted from USHistory.org and I believe I've read it elsewhere when looking up info on displaying older flags, though it doesn't seem to be in the Flag Code nor the aforementioned executive order that dream_face posted, but it certainly seems within the overall feeling for those two documents. Thus, assuming it is fit for display and not "unserviceable", it seems to be perfectly appropriate to display something like, for example, a 13-star, 48/49-star, or one like this particular 33-star Flag which interestingly has the stars arranged in a star formation.

For some other interesting and somewhat-related reading, including how to dispose of a flag no longer suited for flying, there is the US Flag Code and its Wikipedia page, which actually specifies some standards that many people ignore when trying to show off their patriotism. "The flag should not be used as "wearing apparel, bedding, or drapery" is probably the most often ignored, and by people trying to be patriotic and wearing clothes that are basically made out of flags.

Of course there's also some interesting stuff in the Wikipedia article for the Flag of the United States as well.