The first time I was asked to sign a book it was a well-established Australian poet who asked me. So I admitted it was my first time, and asked for his guidance. He told me to open to the title page, and cross out my printed name, and sign underneath, which is how I signed books for a number of years.
Over time I noticed that while most authors do sign their books on the title page, very few (none of the ones I've seen, actually) cross out their printed name first. So I went looking on the internet for instructions on how to properly sign a book.
The most complete information I found was at the blog of author Mary Robinette Kowal. Go to her website if you want a complete tutorial. She did not, however, have anything to say about crossing out printed names, and in fact, I checked quite a few articles and posts written about signing books, and found only two that addressed this issue. Both said that they had seen a case or two of it, but that it didn't seem to be the norm. Perhaps it is an Australian tradition--if anyone knows, I'd love to be enlightened. In the meantime, I've left off with that practice.
My internet search did give me a few pointers that I wasn't looking for, and here they are:
1) Use an ink color other than black so that your signature stands out more. Not too important for the person who initially requests your signature, but if the book is ever resold, it helps those pricing it to notice the autograph.
2) Date all signatures within the first month of publication. This will make the books more valuable someday (assuming there is a market for your books in the future....well, you never know). (Some say, just keep dating after the first month to personalize the signatures more.)
3) Have a different signature than your legal one to discourage identity theft. (I have to say, this seems smart, but really hard to pull off.)
4) In an anthology, sign on the page where your piece appears.
Lots of other tips are available, at Mary Robinette Kowal's website. Beware: there is conflicting advice out there too, such as: the crossing out of the printed name or not, the debate over whether to sign with a stock phrase or phrases or to personalize it more, etc. (It makes it easier for the writer to reuse phrases, but some readers complain if their signed note isn't more personal. On the other hand, some authors report that readers complain if they think a different reader got a warmer personalized note than they did, and so such authors sign everything the same.)
It's an honor to be asked to sign your book, so doing it right matters. Would love to hear your tips and experiences.