Record yourself singing a given song. It will help if it is a song you are very familiar with.
Replay your recording while sitting next to a piano or small keyboard. Identify the note around which the song centers with a simple keyboard. This will often be the last note of the melody of a song; it may occur frequently and may be repeated at the end of phrases. If you're not sure, pick a note that you think is the tonal center.
Play this note at the end of each phrase and play the note with the final notes of the song. If it blends in, or harmonizes, it could be the tonal center. If it doesn't, you've likely chosen the wrong note.
Figure out if the key is major or minor. Any key can be one of these two variations. For example, if you're singing in the key of C, you can be singing in C major or C minor. To determine this, start at the tonal center and count up four half steps. This note will be the third of the key. For example, in the key of C, which is based on the scale C-D-E-F-G-A-B-C, E is the third.
Look for the third of the scale. When you find it, check to see if the third is four half steps away from the tonic (another word for the note that is the tonal center). If the third is usually four half steps away, then you are singing in a major key. If the third is three half steps away, you are singing in a minor key. If both variations exist, look to see which happens more often, as this will most likely help you determine the key correctly.