Find the type of dance you are interested in learning and listen to different types of music, research the costumes, and watch samples of choreography. There are many styles of Oriental Dance, from Tribal/Folkloric, Cabaret, trance dances, to ceremonial dances from many countries. Larger countries have many regional dance forms.
Watch some performers demonstrate the type of dance you are interested in. YouTube has clips of performances, sample classes, competitions and dance scenes from films. Egypt's Golden Age of Cinema produced films which featured Arabic music and dance, starring actresses/dancers famous the world over for their technique and style. Clips from these films which feature dance are readily available on YouTube, so you don't need to watch the entire film to see the dance scenes. Dance companies and schools also have sample videos or classes on their websites. Search for schools and studios near you and see what you can learn from their websites, and maybe sign up for a class as well.
Mimick the movements you see in videos, but do them safely. When learning by yourself, don't attempt difficult moves that may cause injury. Backbends, splits, contortions and any complicated moves you may see in professional performances or in competitions should be learned in a dance class under the supervision of a qualified teacher. Stick to learning simple moves you see on the Internet. Make sure you are warm, wearing comfortable clothing and have adequate space to dance. Learning the basics, such as rhythms, simple footwork, belly rolls, shimmies, posture and arm and shoulder work can give you a base to then improvise and create your own style.
Dance with props.Props can be especially fun to work with and are safe to experiment with on your own. Dance props such as veils, finger cymbals, swords or jugs to balance on the head are all used in performances of Oriental Dance and provide limitless opportunities for creativity.
Find some music that inspires you; there are many musical styles from the Middle East, North Africa, Central Asia and Eastern Europe that accompany belly dance, from Moorish melodies from Morocco, drum beats from Tunisia, orchestral fusion works from Egypt, Algerian Rai and contemporary Lebanese pop. Free-style and improvise, add your own personal style and let your creativity show through your dancing.