When the petals become soft and wilted (assuming the plant itself isnt wilting too) and the flower stem is green and does not fall off when you touch it, this means the flower has set fruit.
Now assuming it doesnt abort later (stem turns yellow and falls off) the pepper under the petals should start to grow, and eventually push the petals off, or sometimes grows right through them (wearing them like a hula skirt).
The stem should also get larger, and eventually the pepper itself will start to pack on some serious weight and should be visibly larger every day.
Early on, for most peppers, the pod will take on a dull, bumpy appearence, and when it reaches full size, it will become more smooth and shiny.
Once it has reached full size, depending on the species, it could take anywhere from a few days to a month to ripen.
Hope that answers your question