The fourth tone is a diatonic tone which is based on βου. The proper isokratima (drone) note for this tone is also (generally) on βου. Use of νη as the vasis of this tone (which we often encounter, especially in "harmonized" Byzantine chant) generally demonstrates a basic misunderstanding of the fourth tone.
When applying the fourth tone to a text, a comma or semicolon in a phrase should end on δι or ζω, or occasionally on πα. A full stop (i.e. period) should almost always end on βου. The exception to this rule is in the slower stikhiraric tempo, in which the full cadence often falls on πα. However, even in the stikhiraric tempo, the final cadence always falls on βου.
In this tone (and in its plagal, the eighth), the law of attraction of sounds is especially misunderstood. Many chanters mistakenly flat all the ζω's. The law of attraction of sounds states that in ascent, the ζω is natural, but in descent it is flatted, because it is "attracted" to the lower note. In practice, the way to apply this law to the fourth (and eighth) tone is usually this: if a phrase ascends to ζω and then descends again, the ζω is flatted; but if the phrase ascends past ζω, it is not flatted, even when it descends again. When applying this rule, it is also helpful to look at the whole phrase to see if it ascends past ζω, rather than just at a run of two or three notes.
There is also a soft chromatic mode of the fourth tone (for details, see the second tone). This mode is almost always employed for Apolytikia and Kathismata. The vasis is still on βου, but there is also a strong melodic center surrounding δι.
An exception to the above rules is the special melody Κατεπλαγη Ιωσηφ, which is in the hard chromatic mode starting from βου and based on κε. This melody is one of the most common melodies for kathismata in the fourth tone. However, when this special melody is prescribed for Apolytikia (for example, the forefeast of the Nativity), the melodic line is entirely different and is in the soft chromatic mode based on βου.
The simplified apikhima for the diatonic mode of this tone is as follows:
βου γα δι κε δι γα βου
(The apikhima is a mnemonic device which the chanter chants before a hymn written in that tone in order to "get into" the prescribed mode. Other apikhima may be found in Greek and Romanian sources. Many of these can be quite helpful but are not so easily memorized.)