1) Order/purchase the cards you will use now. This way you don't have to scrounge after the wedding and you can fill them out at your leisure.
2)Order extra cards, especially if you are using a monogram or personalized name card. These will cover you for all the "Dear Uncle Sarah" slips of the pen. These cards are great to have around anyway for when you give people gifts.
3) Keep a list of every gift you received. Start it now. This instant. The minute you get a gift start the list and keep it somewhere you will not loose it. I suggest using google docs or the thank you manager that comes with your registry so you and your fiancee can both update it. Plus unless the internet is destroyed you will not loose it. And let's face it, if the entire internet is destroyed no one is going to remember about your thank you notes. Write the persons name, the gift they gave you, and if you have it, their address. This will help you personalize the note you write. Look at the card for the correct spelling.
4) Remember that massive list of addresses that you compiled to put on your invitations? Use it. Print all the addresses on clear labels and store in a safe place. When it's card time you can just slap them on.
5) If you can't manage items 3 & 4 at least keep a shopping bag where you throw in all the cards from the gifts you receive. If you loose those them, you are toast. (Unless you have an amazon registry. They have a thank you manager that updates automatically).
6) Fill some out now, in your spare time. You can mail them after the wedding.
7) Buy stamps. Many, many stamps.
8) The early bird catches the worm. I cannot tell you how many people commented on how quickly they got my cards. They still remembered it six months later. If you are not going away then start writing. Carry the cards around to school, to work, and fill them out in your spare time. If you are going away fill out as many as possible before and finish the rest immediately upon returning. I found that it took me forever to fill out the few cards that I did not get out early. Procrastination is a tough habit to break.
9) Recruit your husband if you think his handwriting is passable.
10) This is not really a tip on being efficient. It's a tip on not being tacky. For the people who gave you cash and/or checks do not under any circumstances write "thanks for the money" or something of that version. "Thank you for your generous gift" is much easier on the ears. For others you can mention the gift by name "Thank you for the lovely Challah knife. We think of you every week when we use it on Shabbat" is sweet and personal.
Remember these thank you notes actually mean something to people. Some people use it to make sure you got the gift (Especially people who give you an envelope of cash during the dancing). Others just take it as a sign that young people are not forgetting the niceties of society. Are they frustrating? yes. But if you follow these tips and fill them out as they come in they will be much more enjoyable.