There has been a lot of interest in stepping up to the Arduino by PICAXE users. Since the Arduino programming laguage is "C" like and not "BASIC", there are significant differents in the rules and format and it can be a difficult change.
The are a lot of good books out there on Arduino Programmng. I came across one that is a free download and does a great job in explainining how to program the Arduino.
The book is called "Open Softwear" and was written at Malmo University School of Arts and Commumication. The book was written for pwople who want to make "wearable" microprocessor circuits and does go into their construction. But the second part of the book has a great section on programming.
Here is the link: