The problem with trying to correct a wedding invitation is that you don't want the result to look like someone screwed up and only noticed as the invitation was going into the envelope. After all, if the bride had wanted invitations that were just scribbles of black ink on a card, she could have had them printed that way!
At the same time, you don't want to add such a long, involved explanation that guests wonder "what went wrong?" all the way through the ceremony and miss the vows. And you also don't want your changes to get lost in the invitation envelope, so that guests arrive at the wrong place and time.
One solution is to have the invitations reprinted. In most cases, you'd only be reprinting one card -- not the envelopes, and not the inserts -- so the total cost for reprinting will be well under $200 even with a rush order. If you're on a very tight budget, $200 isn't chump change, of course.
A second solution, if the changes are bigger than a typo but smaller than a complete rescheduling of the event, is to cross out the incorrect information, using ink the same color as the original printing, and write in the new information. This plan requires a helper with nice handwriting and a lot of patience. And it won't look as good as the original invitation did. On the up side, the guests will see the corrected information as soon as they look at the invitation. And you can always hope that, looking back years from now, members of the wedding will see the handwritten correction and remember fondly the hassles of wedding planning. (A printed slip, pasted over the incorrect information, is a little neater.)
A third solution, and probably the one most people will choose, is to put together a card to be photocopied and included in the invitation. This card should be too large to ignore: fitting four cards to one ordinary sized sheet of office paper is about right. Do the card on your computer, and have it photocopied onto cardstock (the stiffer paper) that is a color compatible with the wedding invitations.
And what does this card say? Keep it simple! Unless something truly peculiar and inconvenient is afoot, don't get involved with explanations. Just state the facts:
"The wedding of Susan Price and Thomas Bushnell will take place at Holy Redeemer Church, 426 Third Street, Niskayuna, New York, rather than at Helpful Shepherd Church as previously planned."
"The wedding of Maria Simpson and Carlo Rintacta will take place at 2:30 on Saturday, June 30, rather than on Friday, June 29, as previously planned."
"The wedding reception of Elaine May and Lancelot DuLac will take place at the Veteran's Memorial Hall, 1326 Snelling Avenue, Saint Paul, rather than at the University Club as previously planned. The reception will start at 6 p.m."
You can make the card look more formal by dividing the text into lines that mimic the layout of the wedding invitation, and by centering the text -- but personally, I wouldn't do that. The uncentered text, in natural lines, draws attention to the fact that this card is something different, possibly important.
Had the invitations already been sent, you would have needed to write, email, or phone guests with the new information. These changes can "properly" be made informally, through channels like phone or email. However, it's important that you choose a method that's likely to actually reach guests! Don't rely on email unless you're sure that everyone checks it. It can also be useful, especially with extended family, to set up a telephone tree so that you don't have to make all the calls yourself.
No matter what method you use to communicate changes, do make a point of checking in with the friends and relatives who are most likely to be confused, forgetful, unobservant, or just plain flaky. You know which ones they are! Give these people an extra call or email, or bring up the wedding changes in face-to-face conversation, just to make sure that they actually "got the message" about where they're supposed to be, and when.