Ok, you've got various different strategies for reading music. Remember that music is in 'real time', so, just like reading aloud, you don't want to be starting and stopping, you want to keep the flow going.
Sight recognition - this can be done in 2 ways - either - that dot on that line is an A, this key/finger is A, therefore that's what I play, or more succintly, that dot represents that key. Familiarity makes this correlation faster until it is done instantaneously.
Sound recognition - this is how dd plays when she is learning - she knows what a written note sounds like on the piano, and finds that note before starting. I'm not convinced she knows the names of the notes on the piano, but she could sing them, and given written music could sing the pitches accurately. If they know the tune that can also help guide them.
Numerical - the notes are read in the context of hand position - each finger numbered 1-5 - this enables them to quickly learn recognisable tunes, as it can be discouraging otherwise.
Pictorial and contextual - what does the line of music look like? Are the notes going up or down generally? By jump or by step? Are they fast notes or slow notes (shown by spacing). Is the line smooth or jagged? Where is a note in relation to its neighbour?
That sort of thing really. The aim is to get the processing from eye to hand as instantaneous as possible, and different children respond better to different approaches. The only thing you really can't mix and match is suzuki and traditional as suzuki doesn't introduce any notation till much later on, and children do seem to struggle if they swap between the 2 (I don't teach suzuki).
Hope that's of interest! It's only a broad overview and sometimes I find myself inventing new ways if it works with a particular child. Away from the piano, a certain amount of theory helps (writing down notes etc), but I try and keep it as piano-related as possible so they can see the relevance.