I am playing a piano piece that tells me to use the pedal (it says (with pedal), but it does not tell me when I need to stop, nor when to release and reapply. The piece has double bar lines four measures later, but I feel like it is too soon to stop there. The only other logical place is 50+ measures later, but areas in between there do not seem to require it. Should I stop at the double bar lines or at the next section?
An indication of with pedal or con pedale or pedal ad lib. is a way of expressing that pedaling for a given passage is up to the discretion of the performer. If there are other pedaling indications, then those indications supersede the original indication at the appropriate time in the music. If not, then the pedaling is understood to be at the player's discretion throughout the piece.
In terms of figuring out exactly how to pedal is exactly your problem. As a performer, you need to make choices. You can make choices that fall in line with convention, recordings you have heard, or advice you get from other performers. However, when composers notate with pedal, it is understood that they're accepting of a bit of flexibility (or are simply to lazy to write out specific pedaling).
Hope that helps.
The pedal will sustain any notes played after it's pressed. If those notes combine to make a chord, which maybe can't be held with fingers, then that's the main reason for using the pedal. When the harmony changes, it will sound pretty awful if the last chord sound continues, and bleeds into the next. Thus, a change of pedal will be needed at that point. Ears will tell, if knowledge of chordal theory won't.
'With pedal' instructs you to use the pedal with discretion to achieve a legato effect. It doesn't instruct you to push it down and leave it down! It doesn't instruct you to over-use it, blurring the harmony. You will make much use of the technique known as 'changing the pedal' - lifting it as you play a new note or chord then 'catching' them by immediately depressing it again.
General rule - even if the instruction is 'with pedal', you're probably using it too much!
Schumann gives such instruction a lot. The genre and period of the piece you are playing matter. Normally, you change pedal by the same judgment as you do normally. If there were no "with pedal" instruction, how will you plan the use of pedal? With "with pedal" instruction, it stresses the role of pedal, but it does not mean you have to use pedal everywhere. Usually, when the chord changes, you raise the pedal upon playing the first note, and quickly hit pedal afterwards. When dry effect or clear articulation is intended, you do not use pedal there. If you have further questions, consult anyone with reasonable piano playing experience. Hope this helps.
A basic rule of thumb, or should I say foot, is to lift and restep at all changes of harmony. Now, this sounds technical but it's not that complicated: It's a matter of watching the lowest bass note in the music. (It actually should be done by ear.) Take a look at a copy of Beethoven's Fur Elise. The first, lowest-sounding bass note is an 'A' you'd want to step the pedal down and hold it until the low 'E' arrives in the second measure. At the split second that you strike the 'E' lift the pedal WHILE YOUR FINGER IS HOLDING THE 'E" down and then step back down again. The changing of the bass notes from 'A' to 'E' are changes in harmony, so the trick is to get rid of the old harmony sound by lifting the pedal and stepping back down for the new harmonic structure. I call it 'taking out the trash' - if the piano sounds blurry, murky and underwater, it's time to lift and QUICKLY restep the damper pedal. Now, when you get to the bridge, there are more harmonic changes happening more quickly than previously; so you would lift and restep for the 'C' bass then the 'G' then the 'A' and the 'E'. During the following octave 'E's', the pedal should be held down for all of the 'E's' because they're all part of the same harmonic structure. The repeating, chromatic D# E D# E D# E could go either way, depending on your type of piano (electric or acoustic), the reverberation rate of the room you're in and it could simply be a matter of personal taste. The same goes for the opening theme, there are chromatic D#'s to E's that I would pedal if playing an electronic piano but would not if on an acoustic piano.
Quite simple, in this situation, I think you should go with the flow... Although I would keep the pedal on and release it at my discretion. Just remind yourself what the pedal does: it creates a legato effect for the notes played for the period it is held, creating near-silence upon release.
I said "feel there needs to be a breath" on my last edit. I in fact meant "whenever you feel it is suitable". Sorry for any misunderstanding...