No way we can give you a good advise unless we know those details.
If you are an EU national, you can move to Slovakia. That includes if you are or can get Slovakian nationality through your father.
If you are not EU/EEA, having your father born there will not be enough to move.
You might have the right eduction to get a job in Slovakia, for which you can get a work permit.
Getting an other nationality is not simple, takes many years and it is not even certain that you will want it.
If your father was a citizen of Slovakia and is still alive to sign papers for you then maybe.
My husband did this for our son who was born in the USA.
Husband had to prove his own citizenship and then fill out tons of forms for our son. This was done 20 years ago but I have heard that now because of being part of the EU, you must now also go into the embassy and have your fingerprints taken.
Best bet is to call up the Slovkian embassy in your area and ask them how this can be doen and what papers they want from you.
I know that some people who's parents or grandparents were born pre soviet times have a hard time proving where their roots are from.
My father was born in Poland, I now live in Hungary, perhaps I should check out if I could be a citizen of Poland, just a thought.
If your father was a citizen of the Slovak Republic you can apply for citizenship and get a passport. You must have a Slovak passport before you go there, otherwise you will only be allowed to stay in the country for three months. You can check this information on the website of the Slovak Embassy in your country.
Yes, just like you can move to any other country in the world.
But, if you meant to move there and become their citizien, you'll need a lot of papers that say you have the right for it, and you should know the language. No language, no papers.
You can move to any country you like but I suppose you mean also getting the nationality too. That can be easy as long as you have the proper documents of your father's birth place and that of his parents.
Depending your current nationality it may be better not to give it up or even better to keep both.
