Hire an accompanist if you do not play an instrument. This can be a piano player, guitarist or anyone who is skilled with a particular instrument. The accompanist you choose should be familiar with basic chord structures, standard pitch tuning and know how to transpose keys. If you're working with a guitar player, proficiency with using a capo is desired.
Give the accompanist sheet music or a recording of the song you want to sing. Allow time for him to practice the song a few times in standard tuning and become familiar with the chord changes.
Rehearse the song with your accompanist playing along. Start out by attempting to sing the song in the current key. If you find yourself straining to hit high notes or the key does not feel comfortable in your range, ask the accompanist to transpose the key down two steps and then try again. Or if you're having trouble hitting the low notes, transpose the key up two steps.
Practice the song several more times in different keys until you find the one that best suits your voice. Ideally, you want to find a key that brings out the strongest natural part of your vocal range and tone. If you've chosen the right key, you should be able to hit all the notes with plenty of air behind them in the low register and no vocal "cracking" or straining in the high register.
Experiment with finding a few different keys that work for each song. You might ultimately decide to record the song in a higher key, but lower the key when performing live. Many professional vocalists drop the key of a song in live performance because singing in the original key night after night might be too strenuous for the voice.