Hi Ted,

There are many ways to modulate among keys. The two most common methods are moving from the current key through the dominant of the new key, then continuing the melody in the new key; or, using a diminished chord common to the current key and the new key.

In the first instance you would move from an Eb chord through a C7 chord to an F chord. In the second instance you would move from an Eb chord to a F# diminished chord and then to an F chord. Which method you use will depend on the melody notes.

Finally, there is nothing wrong with a song beginning in F and ending in Eb. It may not be common but it isn't wrong. The only guide is how the music sounds to you. If it sounds good as is, then don't modulate back to F. However, you are asking the modulation question and that leads me to think you feel your song needs to return to the key of F.

If I can help you further, don't hesitate to ask.

Chuck