Summarize:

When you choose a song that you'd like to sing a cappella, you'll need to listen to it thoroughly to truly understand everything that's happening in it. Listen to it multiple times, getting a feel for the lyrics, rhythm, and different instruments that all make up the song.  Starting with a simple song you know by heart will make it easier to arrange. Look online for the song without instruments by searching for the name of the song plus "vocals only." Most songs have long instrumental solos or parts that just don't work when you're singing it a cappella. Decide which parts of the song you're going to cut and which you're going to keep, making sure you string the sections together so that they flow smoothly.  If you need help doing this, look up videos of other people's a cappella arrangements to see how they condensed the original song. It's helpful if you cut up the actual song using a computer system so that you're able to play it over and over again once it's condensed. This includes the solo and all the verses you'll be including in the song. If you're able to read and write music well, write out the notes for the bass as well as any other instruments you're hoping to include in the arrangement.  You may need to experiment with several different versions of your arrangement until you discover one you like. If you can't write sheet music, use a computer system to split up the different levels of the song so you can arrange it that way. If you aren't experienced with arranging music, look online for an a cappella arrangement for the song you want to sing. Your sound is your main priority, but spend effort on other visual aspects such as facial expressions and choreography. Once you're satisfied with your singing, work on the movements you'll be doing onstage (if any) and on expressing the song through your facial expressions as well.  All dancing should be well-practiced and fit the song's theme — a quiet heartbreak song might do well with you standing still, while an upbeat song can have dance moves incorporated. Use your face to express the emotion in the song. If you have lots of energy and grin during a happy, upbeat song and look serious and sorrowful during a sad song, the crowd will take you much more seriously.
Listen to the original song carefully beforehand. Condense the song to fit in a cappella format. Write out the lyrics and musical factors that make up the arrangement. Hone your performance.