First of all I need to mention - there are residence and citizenship.
Residence - it's when you have right to live in Ukraine, work or study, but you can't vote, Ukraine is not responsoble for you in some situation and you can't pretend on some social welfare.
Citizenship - when you are true citizen of Ukraine and can recieve everything from this country.
How to become a resident of Ukraine
You can apply for residence if you come to Ukraine for studying, working, family reunited, volunteering, religious activities, scientific, educational activities and other things. I think if you read this article, I already mentioned your purpose.
At first we need to understand: there are permanent and temporary residence.
You need permanent residence if you want to immigrate and live in Ukraine for rest of your life.
You need temporary residence if you want just study or work some years in Ukraine, and than return to home or move to some other country.
3. Reuniting with family (with ukrainian wife or husband);
4. Work in religious organization;
5. Work in offices and branches of foreign organizations, companies or banks;
6. Cultural, educational, scientific and volunteer activities;
7. Correspondent work or representative of foreign mass media (MSM);
After 10 days when you come to Ukraine, you need to register where do you live. For this you need to provide documents of renting apartment, ownership in Ukraine or else. In case you don't do this, you will be judged and need to pay fine. So all students and people who want to work in Ukraine need to prepare this documents before they will come to Ukraine.
You must notice, that in any case you need to have translated passport into Ukrainian language, insurance policy and pay fee for residence (few dollars).
Very often agents insure students, after they come to Ukraine, they will easily find work, and can cover some costs for studying, but it's not true! FOREIGN STUDENTS DON'T HAVE RIGHT TO WORK IN UKRAINE. Legally of course. But work illegaly is dangerous, because you can easily be deported from Ukraine.
Permanent residence (immigration)
For premanent residence you need to recieve a permission for immigration. Than you will recieve immigration visa. This visa is valid for 1 year. Thanks to this immigration visa you have the same rights for job as Ukrainians, you don't need to pay medical insurance, you can easily come and left Ukraine, and you don't need to prolongate your permission. It's permanent residence for all life.
In which case you can get permisson for immigration for permanent residence:
1. If you have Ukrainian wife/husband and live in official marriage fat least 2 years;
2. You are very cool culture and science activist, which need Ukraine;
3. Highly skilled professionals needed by Ukraine;
4. You invested in economy of Ukraine not less than 100 thousand. dollars;
5. Brother, sister, grandfather, grandmother, grandson, granddaughter are citizen of Ukraine;
6. Persons who were Ukrainian citizens previously;
7. Refugees (after 3 years of residence);
How to become citizen of Ukraine:
1. You need to born in Ukraine.
2. Acquiring the citizenship of Ukraine by territorial origin. If one of your relative (parents, grandparents and others) was born in Ukraine and live there till 24 August 1991.
3. Accept Ukrainian citizenship. To become a citizen of Ukraine using this way you need:
1) refuse of your citizenship
2) live in Ukraine for 5 years or live in marriage with Ukrainian citizen for 2 years.
3) recieve a permission for immigration.
4) pass exam of Ukrainian language
5) show that you legally earn money for living in Ukraine.