Eliya...my corrections will all be in red and recommendations will be in blue:

My volunteering

I'm going to tell you about my volunteering with in an organization called, "Anonymous For Animal Rights".
The goal of this organization is to help the farm animals in Israel.
We are doing it in some several ways., I will tell about few of them.
At first we are helping people to go vegan, or at least to reduce the consumption of animal products, by   through workshops for exploring veganism.  , or oOur big project, - is "Chalenge 22+" in which interested people experience veganism for 22 days, with a lot of help from dietitians and people who are have been vegans for along time.

In addition, Anonymous is trying to change the laws about regulating the conditions of the farm animals.
For example, right now most of the eggs come from battery cages, which are very cosy,(I am not clear what you are trying to explain here.  Perhaps, someone else who also knows something about your project will understand better) and we trying to take it out of tha lawmake them illegal.
So We have petitions and demonstrations about things that are not okay in keeping with our strategy to for achieve our goals.

That's it for now..
Thank for reading and correcting :)