If you or the author will be selling books on the day, send out letters to parents so that children can bring sufficient money into school on the day. If you can cope with the organisation involved, you may wish to take orders in advance.
The visit is likely to produce a surge of interest in the author's books, so make sure your library is prepared. It may be sensible to invest in a few extra copies.
The arrival of someone even remotely well-known tends to produce a stampede for autographs. To save disappointing your children, it's a good idea to talk about this issue with the author in advance. Some authors are willing to sign anything (which takes time), some bring signed bookmarks or postcards with them and some prefer not to sign autographs at all.
Check with the author about what equipment they will need during the talk. If they are running a workshop, you'll also need to know what equipment the children will need.
Make sure the office staff know about the visit and who to contact when the author arrives. A staffroom can be a lonely place for a visitor. Try to organise someone to keep them company, make sure they have something to drink and find the toilet.
Organise someone to show the author to the relevant rooms and back to the staff room afterwards. An unfamiliar school is a very difficult place to navigate.
Arrange for the usual teachers to be present during the talk to control behaviour. It sets a good example if they actually listen, rather than mark books.
If the author is giving a workshop, make sure that the children have all the necessary materials available and that the room is arranged in a suitable way for the planned activities.
A brief thank you note is always welcome. Multiple letters from all the children make a useful writing activity and are fun to receive. But they are definitely not compulsory.