Books are still very important for kids to learn how to play chess. It will be more effective to be used together with chess software. Since software can be made more visual and interactive, kids can learn chess by using software even as young as 3 or 4 years old. Kids can read some chess book for absolute beginners especially written for young kids at age 6 or so. But most kids will really be benefited from chess books after 8 or 9 years old when they have developed decent reading skill. The chess books listed in Chess for Beginners should be enough for most of kids.
If your kids are really interested in chess and perform well in school chess club or program or local scholastic tournaments and want to improve beyond beginner level, Winning Chess Tournaments for Juniors is an excellent book for scholastic chess tournament players.
If your kids are scholastic tournament players and have an USCF rating above 600, tactics is the first specialized area to start.
If your kids are scholastic tournament players and have an USCF rating above 1200, they can read more chess classics or specialized books in following areas:
