To illustrate how accents may be produced on your iPhone, let us trace through an example of how to produce the character, ü.
Look up the unaccented version of the character you are looking for.
Press and hold the character; each of the character's accents will show up as seen below.
While continuing to press on the screen, slide over to the accented character you desire (in this case ü).
Now, let go of the screen and the character will show up.