If having small hands makes it difficult to play even standard chords on your guitar, there's no need to give up on the instrument. A shorter guitar or a guitar with a narrower neck would make playing a bit easier. Adjusting the action of the guitar also might help -- if the strings are too far from the fretboard, they'll be hard to push down for a clear tone. Finally, strengthening your fingers can improve your sound and your technique.
Guitar Scale and Size
The scale of the guitar affects how far apart the frets are. The scale is the entire playable area of the strings, from the nut, which supports the strings at the scroll or head of the guitar, to the bridge, which holds the strings in place at the base of the neck and transfers the vibration to the body of the guitar. The farther apart they are, the more difficult it is to form chords if your fingers are short. If stretching your fingers from first to third or fourth frets to make a chord proves difficult, a guitar with a smaller scale length will be easier to play. The scale length of a standard or full-scale guitar measures 650 millimeters, while a slightly smaller length is only 640 millimeters. Try guitars with different scale lengths to find one that feels comfortable to you. Likewise, a smaller version of the entire guitar might better fit your hand size. Ask a guitar-store representative for permission to try a 7/8- or 3/4-size guitar to see how it feels when you play it.
The neck width also affects how hard or easy it is to play notes clearly. If you play an acoustic or a classical guitar, switch to an electric or narrow-necked guitar temporarily until you get more comfortable playing notes and chords. Once you've built up a little strength and agility, switch back to your original guitar. If you play or practice too long with an electric or narrow-necked guitar, however, an acoustic or classical guitar may feel almost impossible to play well.
Adjust the Action
The action of the guitar -- it's playability -- determines how much pressure you must put on the string to create a clear-sounding note. If the action is too high, meaning the strings are too far from the fretboard, you must exert a lot of pressure to hold down the string to create a clear note. Low action makes the guitar easier to play, but if it's too low you'll hear fret buzz from the strings touching the frets. Take your guitar to a professional who can adjust the action for you if you feel it is too high. A pro also can tell whether the neck requires other adjustments that may improve the guitar's playability.
Strengthen Your Fingers
Strong fingers create stronger, clearer-sounding notes, especially when it comes to making chords. Exercise your fingers by placing the first finger on the first fret on the fattest string -- the low E. Keep your finger curved so just the fingertip presses the string. Place your middle finger on the second fret on the same string, your ring finger on the third fret and your pinky on the fourth fret. Pluck the string to ensure that the notes sound as they should. If you keep your fingers slightly rounded and do not move them as you place each subsequent finger on its respective fret, the notes will sound clearly. Keep repeating this process, moving your way up to the fifth string, the fourth string and so on to the first, then back down to the sixth or lowest string. The more often you do this exercise, the stronger your fingers will become and the better your notes will sound.