WE start learning Hiragana and Katakana in kindergarten (age 3-5), and start learning Kanji in elementary school (age 6-12). In elementary school, we learn about 1006 basic Kanji. They say we neet to read and write about 3000 Kanji to live in Japan without any problem in general.

Just adding to Yuri-san's answer... I'd say you need to read, write, and understand about 2000. That's what you need to pass JLPT level 1. Also, Kanji Kentei(Kanji test intended for Japanese) level 2, which is barely good enough for business, requires 2136 kanji that we are supposed to have learned when finishing high school (age18). After that, you don't really need to be able to accurately hand-write all. Native Japanese speakers, too, make mistakes, forget, look up when actually writing, even though we kept studied up to high school. (Just like English speakers make mistakes on spelling.) In most cases, we can use computer or cell phone to write. Being able to read, or at least knowing the meaning, is more important.

OOPS, sorry, your question was "At what age...". I thought I read "At what grade..." at first. In that case it has to be at pretty young age...

As far as I am concerned they start learning it since they are in grade one. It's because the Kanjis are usually divided into 6 grades. Grade 1 includes only 80 basic and useful (and easy) Kanjis. It might seem impossible at first, but Kanji is actually pretty easy to learn once you get the hang of it and the techniques to remember them. I hope this helped. I also hope any native Japanese speaker gives any correct answer if mine is wrong. ^_^