It's quite hard to answer this question and the best would be to follow a flora, which I'll not just copy informations from to past here.
So following are general observations subject to numerous exceptions.
Hieracium generally have lanceolate to oval leaves, not or little toothed, most hairy.
Crepis and Leontodon have generally Taraxacum-like leaves, that means, dentate to lobed.
Some Crepis have leafy stems (but some don't), while Leontodon always have their leaves concentrated to the base, forming a rosette.
[edit on 2014, october 2]
Be aware that there is another genus of the Asteraceae family which may be mistaken with the Crepis/Leontodon/Hieracium group, although it's easier to distinguish. It's the Hypochaeris genus.
Hypochaeris have few but not so homogenous species as there are within the other genera.
Hypochaeris radicata (which may be the most common species in France and wester Europe) have all its leaves basal, forming a rosette and sticking to the ground (never erected). These leaves are always lobed (neither entire, nor toothed), with erected hard hairs covering there upper faces.
Hypochaeris maculata may be mistaken with some Hieracium : it have hairy smooth entire leaves wich are (all or mostly?) basal forming a rosette.
[Addition on August, the 5, 2014]
Also Leontodon and Hypochaeris have hollow stem just below the capitulum(1). When you press the stem just below the capitulum, you fell it flattens under your finger, and if you use the nail to make an incision in the stem, you will see it is hollow like a pipe.
NB : Taraxacum also have hollow stems but they are fully hollow (from the base up to the capitulum), while Leontodon just have the upper part of the stem which is hollow.
Leontodon are almost always monocephal, that means, the stems are not branched : they have only one capitulum per stem, while Crepis and Hieracium and Hypochaeris mostly (if not always) have branched stems carrying several capitula.
(1) the capitulum is the type of inflorescence in the Asteraceae family. It's also called "head" (and actually, "capitulum" is the latin word for head).
You may like to have a look at this page [in french] presenting some common yellow and ligulate weeds from the Asteraceae family to get some illustrations of what I explained here.