How do I apply for American citizenship?

The U.S. citizenship law has changed over the years. The law that was in place at the time of your birth is what will be applied in your case. Without knowing in which year you were born, I am assuming that the law in effect for persons born between December 24, 1952 and November 14, 1986, may apply to you. Under this law, you would be a U.S. citizen (even though you were born abroad) if all of the following conditions are met: 1. Your parents were married at the time of your birth (for children born out of wedlock, the mother had to be a U.S. citizen for the child to acquire U.S. citizenship); 2. One of your parents was a U.S. citizen when you were born; 3. Your citizen parent (in your case your U.S. citizen father) lived at least ten years in the United States before your birth; 4. A minimum of 5 of these 10 years in the United States were after your father's 14th birthday. If you meet these requirements, you can then apply with the USCIS for a Certificate of Citizenship. You must attach documentary proof that you meet all of the above conditions for acquiring U.S. citizenship.

Assuming that you qualify for US citizenship at birth, you can apply for proof of your citizenship by applying for a US Passport with the Department of State on form DS-11 or you can apply for a Certificate of Citizenship with the Department of Homeland Security on form N-600. You will also need to submit your original Birth Certificate, your father's original Birth Certificate, your father's original Marriage Certificate, and proof of your father's residence in the US for a certain number of years prior to your birth. Proof of residence can include, but is not limited to: junior high/high school/college records, medical records, tax records, bank records, employment records, etc. A US Passport will cost about $100, while a Certificate of Citizenship will cost about $600.

You may be eligible to become a US citizen through devolution. It is a fact intensive procedure and whether you can in fact obtain US citizenship on the ground that US citizenship status devolved on to you from your father will depend amongst other things on the applicable law at the time of your birth. Without more information about you and your father's history, I am unable to conduct the necessary inquiry about your eligibility for US citizenship by devolution. Next, if you have in fact been living in the US since 1960, another option is for you to file Form I-485 Adjustment of Status application [green card] under s.249 INA; 8 U.S.C.s. 1259. If your green card application is approved, [hopefully within 6 months, you may within 5 years thereafter file to become a US citizen in your own right. Whichever of the options you elect, I strongly urge that you consult in detail with an experienced immigration attorney

Procedure and the costs will depend on multiple factors, starting with the date and place of your birth, whether your parents were ever married, etc., etc., etc. After trying for 7 years, perhaps, it might make sense to invest $150 into a consultation with an immigration attorney.