To modify means to describe, modifiers need to attach themselves closely to the phrase they describe.What is a modifier ,an adjective modifies a noun eg yellow flower ,yellow modifies the flower so yellow is a modifier.
Wrong: Sifting the sand of a river bed, gold was discovered by prospectors in California in 1848.
now you see the problem here ,the sentence is saying the gold is shifting the sand,which is cannot be true.
Right : Sifting the sand in a river bed, prospectors discovered gold in California in 1848.
heere the phrase or clause directly precedes or follows the noun it describes which is correct.
try another one
Wrong: Engraved, printed, and colored by hand,William Blake could make only a few copies of each of his books of poetry.
Engraved ,printed ,and colored by hand refers to William Blake rather than his books of poetry
Right: William Blake could make only a few copies of each of his books of poetry, which he engraved,printed, and colored by hand.
Though i have discussed the dangling modifier i will again refer to it here with this sentence.
Wrong: Desiring to free his readers from superstition, the theories of Epicurus are expounded in Lucretius’s poem De rerum natura.
Now the first part of the sentence refers to theories rather than Lucretius .To check whether sentence is correct ,you can ask the question who expounded the theories.Lucretius is acting as an adjective here.
Right: Desiring to free his readers from superstition, Lucretius expounded the theories of Epicurus in his poem De rerum natura.
Another type of error is he misplaced modifier
Wrong: That night they sat discussing when the cow might calve in the kitchen.
which is wrong misplaced modifier.
Right :That night they sat in the kitchen discussing when the cow might calve.
reference to modifiers
:Kaplan grammar workbook ( i recommend it)