Select the key of the song you want to arrange. Unless you use a capo, this key should be "C" or "G" to allow both hands maximum freedom for movement across the strings.
Begin to play a chord progression, such as G, F#/D or D, Em and C, which is an extremely common and basic musical progression.
Pick individual notes with your "index," "middle," "ring" or even "pinky" fingers once you have determined your chord progression. This should be done on the thinnest, or higher-pitched, three or four strings.
Practice until you develop a melody you are pleased with and can replay it comfortably at will.
Develop an accompanying bass line, which should be plucked with your thumb on the thickest, or lowest, two strings. Usually, your bass notes will be "home" notes, the note that share the same name as the key you play any chord in. In the G-F#/D-Em-C progression, the home notes are G, D, Em and C, but playing the bass as G, F#, Em, C will give it a unique harmony that can be substituted for a D at any time.
Practice the arrangement, playing both parts together, until you have mastered your arrangement.
Write out the guitar tabulature, which is the sheet music of modern guitar-related music reading, if you have a difficult time memorizing music. This can be done while you create the song or after you finish the creation process. You can also record yourself playing the song if you are unable to write tabulature.