This is a broad question, but a good one. There are exceptions, but in general, modernist writers' goals are focused on:
- the replacement of religious certainties, moral absolutes, essentialism, and determinism with skepticism, doubt, and relativism
- a feeling of alienation, angst, and "nausea" about materialism, mainstream institutions (education, work, and religion), role of the individual in society, and the accepted, status quo standards of society
- existence as problematic (i.e., there are no certainties or absolutes about the meaning of life, the existence of God, the traditional pathways to happiness)
Remember, the modernist era began with incredible hope and improvements in technology (the camera, internal medicine, airplane, mass production, industrialization), but it was plagued with nationalism, greed and poverty, and cruelty--all culminating in the worst 30 years in human history (1914-1945), which saw two world wars, a great depression, pogroms and holocausts, and despotism and corruption. The sum total was "engineered pain": we had found a way to kill and torture more efficiently that ever before. So, you can imagine that wholesale changes in beliefs about God, country, and the individual were taking place--most of which were negative and pessimistic, but justified.