New nibs
You are most likely to get problems when the nib is new. This is because the nib comes from the manufacturer with a protective lacquer coating to stop it from rusty. Usually, once this coating has been removed the ink will flow easily from the nib. A good indication of the nib having the protective coat on it is if the ink sits as a blob on the nib.
There are several methods of removing the lacquer and you can read up about these techniques in the Calligraphy #101 prepare your nibs post.
Paper
The choice of paper is always important with calligraphy. When ever possible use a smooth paper to produce a smooth line. A smooth paper will give crisper lines.
Pressure on the Nib
Normally when using an edged nib, you do not want to put too much pressure on the nib whilst writing. Only a very light pressure should be applied. However, a good way to start the ink flowing is to apply a bit more pressure on the nib such that the tines just start to splay. At that point give the nib a very slight wiggle from left to right. You want to wiggle on the spot so no ink marks are made on the paper, just the hand and pen holder move slightly.
Ink
The ink dries up too quickly or you have been idling the pen and nib for awhile (went to grab a sandwich or a drink), blocking the area between the tines. By just “touching” the surface of the water in your water jar with the nib point, NOT submerging the nib, this will dissolve the blocked paint or ink, and off you go again. Ink that has partially evaporated and become “thick” can be diluted with clean distilled water (I find tap water is fine too), a drop at a time.
Damaged Nibs
If a nib is damaged it can prevent the ink from flowing. The tines on smaller nibs and especially small pointed nibs can easily overlap or get bent. Overlapping tines can usually be pushed back in to place. If the tines are bent they can sometimes be bent back in to shape, but it can be quite awkward getting the tines to line up perfectly. Often it will be necessary to replace nibs which have bent tines.