You can get these details online by using any suitable Online Panchang(Panchangam.
Some such Panchangam sites give facility to have your horoscope free online, if you feed the required data like date of birth,(-date,month and year) time, location with longitude and latitude or nearest main city etc.
At least you can have the star and Rasi(Zodiac). Then you can approach a learned and experienced astrologer near you to cast your horoscope. You may also get it verified( Sphutam) by the same astrologer or another experienced and reputed astrologer also, who will apply certain cross testing with your other details.
For example I can give a site where you can get your star-.(prokerala.com/astrology/nakshatra-finder/)
In that if you fed your date of birth, time and location, you get details lik star and Zodiac as per western system and Chandra Rasi as per Indian system. You can also have certain other details too. But take this as only a rough Kundali only, and confirm with an astrologer as said before.