Novice guitar players often use a pick when strumming a guitar, especially if they're playing a steel string guitar. Classical guitars are usually plucked and strummed by hand. Classical guitars have a higher fret board. The strings are farther apart and are usually made of nylon. You can strum any type of guitar without a pick, but this technique is best suited for a classical guitar. Regardless of the kind of guitar you play, if you can strum with your fingers, you'll never have to worry about forgetting your pick.
Hold your guitar in the same manner you would if you were going to strum it with a pick. Depending on the type of guitar you're playing, this means holding the guitar across your lap (acoustic), or on your raised left thigh (classical). You can use a footstool to elevate your left leg.
Strumming is when you play two or more strings in unison, as opposed to picking or plucking them individually. To do this without a pick, use the hard surface of your nail on your index finger (on your right hand if you're a right-handed player; if you're left-handed, strum with your left hand on a left-handed guitar).
Now pinch your index finger against your thumb. These are the two fingers you'll be strumming with. Your thumb adds support to your index finger.
Starting from the thickest string, stroke your index finger down all six strings. Your index finger should be facing the guitar so that the nail is hitting the strings. Practice this until you can sound all of the strings simultaneously. This stroke is called the down stroke.
The up stroke is slightly more difficult because you don't have the protection of your nail against the strings. The up stroke is the return stroke from the bottom, or the thinnest string, back to the thickest. Sound all of the strings together, drawing your index finger up and using the fleshy part of your fingertip to strike the strings. After playing this way for a while, your fingertip should begin to develop a callous, and you'll be able to strum with more force.
Once you've mastered the basics of finger strumming, you should practice strumming fretted chords. This means you might only be strumming two, three, four or five strings at a time, instead of strumming all six. Your index finger will start and stop only on the strings you wish to sound.
There is a difference between finger strumming on acoustic and classical guitars. Steel strings are rougher on your nail and skin than the softer nylon strings of a classical guitar.