Choose a song. Any song, regardless the genre or era it was written can be performed in a jazz style. The most important element to needed successfully improvise is confidence. Choose a song that you enjoy and know extremely well. You have to know the rules prior to breaking them. You must be comfortable with the correct notes of a song's melody prior to rearranging it.
Note the key signature of the song you would like to perform. At the beginning of every line on the sheet music, there will be a number of flats or sharps. This indicates the key of the song. If there are no flats or sharps, this indicated that the song is in the key of C. If you are unsure of the key your song, consult a music theory website such as Ricci Adams' musictheory.net. This is most important if you are singing. You must find a key that comfortably fits within your vocal register.
Note the time signature of the song you would like to improvise. At the beginning of the first line on the sheet music, there will be numbers. This indicates how many beats there are in a given measure of the music. This will indicate whether a song is a waltz, a bossa nova or even a two step. If you are unsure of how to read a key signature, visit a music theory website.
Choose a tempo for the song you would like to improvise. Jazz is a genre that allows you to do whatever you would like when performing. If the song you have chosen is typically performed quickly, there is nothing wrong with choosing to perform it slowly, and vice versa. As you begin improvising, start with a slower tempo. This will make it easier for you to get comfortable making up your own melody line.
Improvise. When you are comfortable with the key, time signature and tempo of a song, it is time to create your own melody. The art of jazz is about doing whatever feels right to you in a particular moment. As long as you stay within the key of the piece you are playing or singing, there are no mistakes. Enjoy yourself.