The Hasbara project is not an official one. There are many separate  and often independent (I'd say "grassroots" but I just love the word too much to have it highjacked) components. "Hasbara" literally means "explanation". It's what many of us at Znet call "Israeli rhetoric". The Goal of the Hasbara project? It depends who you ask:

"...an Israeli-based grassroots initiative. The purpose of the ICIC is to assist efforts to explain Israeli life from the vantage point of the average Israeli citizen."
(Israel Citizens Information Council)

"The mission statement of the Department of Education of the Jewish Agency calls for intensifying the multi-dimensional significance of Israel in connecting the next generation of the Jewish People to its heritage, people and homeland."
(Department of Education of the Jewish Agency)

"THE ISRAEL HASBARA COMMITTEE is an entirely independent media voice that brings you new and highly relevant news, opinions, issues and information every day, five days a week, which relates in some way to the defense of Israel and her image."
(The Israel Hasbara Committee)

"Hasbara Fellowships, a program spearheaded by Aish International, educates and trains university students to be effective pro-Israel activists on their campuses."
(Hasbara Fellowships)

Quite simply, if you sum it all up, the Hasbara is Israel's public relations. It's wide-spread, it's *shudder* grassroots and done individually by people who are trapped in fear of their own making. The best way to see Hasbara in action is talk to an average Israeli. Here's a few statements I picked up on an

Israeli Canadian (Israelis that live in Canada) forum (limited by my translation):

"...you shouldn't hide your origins and religion, but wear them proudly... You need to show the (non-Arab) Canadians how much the Jews are rational, responsible and justice-seeking. You can do this with private conversations, writing, maybe even public action... We mustn't leave the Arab propaganda in Canada unanswered... [The Arabs] may not interest everybody [Canadians, British, French], but enough to mold public opinion, or wake anti-Semitic tendencies, hidden in said Canadians...I heard from French Canadians in Montreal a severe criticism of what Israel did in Gaza, we have to explain it to them... "

Another option is to read the most leftist paper Israel has, Ha'aretz:

"Fearing anti-Semitism, Jews in Muslim lands distance themsleves from Israel's actions."

Let's Get'em While They're Young
The Israeli public education system is in shambles. Graduating rates and grade averages drop every year, while violence in the schools is rising. Maybe some day I'll write a 3000-page book about the direct correlation between content that's being taught in Israeli public schools and the Israel/Palestine "conflict", but until then here are a few examples from memory:

In kindergarten they build your national pride, by celebrating holidays and standing in silence on national mourning days. That sounds like innocent patriotism (if you subscribe to that sort of separatism), but this is when they don't tell you on Independence Day that there are people who call this day Al-Nakbah ("catastrophe"). Or Passover, when they tell you that "not just one alone has risen against us to destroy us, but in every generation they rise against us to destroy us". Or Memorial Day, when we stand in silence in the memory of our heroic troops.

First grade up until twelfth is a balanced diet of self-victimizing and heroism. History lessons distort facts and tell how little ole' us were surrounded by 4 enemy armies in 1948, and kinda' forgets to mention the fact that while we deployed 90,000 troops and were backed by France and England, the four armies deployed 68,000 troops. Literature Lessons teach a line of predominantly Jewish writers and poets (but not the Communist ones, or the pro-Palestinian ones). Arab poets don't exist.

Highschool has several peaks:

• The "Acharai" ("follow me") organization comes into classrooms and signs the kids up to a pre-army-training after-school activities. I admit I've never been to an Acharai session, as far as I understand it, its focus is on physical training, but I believe it's probably a great opportunity to insert some of those wholesome Zionist values.
• The "Gadna" ("youth corps") is a week-long field-trip to an army camp, which is specifically designated for the purpose of you and your friends to simulate basic training. The highlight being, giving 16 year-olds guns and teaching them how to use them. The teaching of use of rifles, by the way, is called "purity of arms".
• The highest peak of an Israeli brat's education is the "Roots Voyage", in the twelfth grade, to Poland. Where Polish, Russian and Moroccan decentness alike, will  find out that a Jew's roots are all in Auschwitz . The idea is to unite us all in fear, for a good group cry (pardon the bitterness, but I was there). Here's something I will never forget, one of my class mates said, by the end of our voyage (limited by my translation and memory):
  

  "I wasn't sure I wanted to get drafted, but now I realize how vulnerable us Jews are, and understand the importance of protecting our country that's surrounded by enemies."
  

Hitler would have been proud.

To close this overloaded post, I'd like to add the words of grassroots Hasbara activist and Minister of Education, Yuli Tamir (Hebrew) (limited by my translation):

"...Because of the (supreme) courts, it's very hard for us to close down private institutes [schools]... In the name of freedom of vocation, the legal system is allowing the religious sector and the Islamic movement to expand and thus harm kindergartens and schools of the public sector... Every private non-profit organization that wants to open up a daycare center gets an authorization, even when it's an anti-zionist organization, or ones that are anti-Israel..."