I'm writing a song where some measures have less than the full number of beats indicated in the time signature. This occurs in the middle of the price, but it is a pickup to the next phrase. How is this normally notated? Do I just write a measure with one beat without changing the time signature, or do I have a measure of 1/4?
If you're putting an extra beat in then yes, the proper way to notate it is to have that measure in 1/4 time.
Also note that the following measure, if its in 4/4, would need to have the new time signature notated as well. That is, one would have to write the next measure with a 4/4 time signature.
Is there a full 4/4 bar before each pickup? In that case it will have to be a 1/4 bar. But this is rare. Maybe you're following a pattern (common in hymn tunes) where each line has an anacrusis but there are no extra beats. Often this is notated with a split bar, often with a line break.In this case no extra time signatures are required.
I've a feeling that you are using anacruces, which are the pick up notes, often of one beat. You MAY just find that the rest of that particular bar still exists, but nothing is happening in it. So, three beats of rest and the one beat anacrucis could be what you need to write. If the pulse of the piece is interrupted for this bit, then I'm wrong. If it continues smoothly, this could be correct.