Most pronoun problems result from ambiguity of reference. Take this sentence: "Odysseus wants to go home and is blocked by the gods, which is unfortunate." What does "which" refer to--Odysseus's desire or the gods' action? Perhaps the writer has in mind the whole idea of Odysseus's thwarted desire; if so, the sentence should be revised for greater clarity.
"It," "that," and "this" are among the worst vague pronouns. Consider this construction: "Homer says that Odysseus is weeping when he is on the island of the sun god and loses all the crewmen. This shows his humanity." "This" is too weak a link between the two sentences; it needs replacing with "The weeping" or an equivalent phrase. A precise reader would also object to "his" in the last example. Does it refer to Homer? Odysseus? The sun god? The only safe procedure with a pronoun (he, she, it, they, they, that, these, who, what, each, every, such, some, many, and so on) is to make sure a pronoun refers unambiguously to a single antecedent, which in most cases will be the closest possible noun. Remember that "antecedent" means "going before."
If you suspect that your reader will not follow your reference, replace the pronoun with its antecedent noun. A little repetition is better than a lot of confusion. In these necessary repetitions competent writers sometimes observe a principle of variation. They avoid repeating the same bare noun over and over by using it in phrases (hence "repetitions" becomes "these necessary repetitions" above) or by substituting obvious synonyms. Used intelligently, variation contributes to good style. Be careful, however. Synonyms are seldom exact and may confuse your meaning. Like any formal device, this sort of variation can be overdone ("He picked up the handgun and pointed the revolver at his victim, whereupon he fired the weapon and then threw the pistol away"). If you use a thesaurus to hunt down synonyms, be sure you know exactly what a word means before you use it.
See also Purdue handout on using pronouns clearly