The Spanish Empire began to settle the Americas after the historic 1492 voyage of Christopher Columbus. Most of their colonization efforts followed a routine: "discovery" of a new land, survey of resources and indigenous peoples, and then colonization by any means necessary. Some colonies settled peacefully, while others were emplaced by military force. In each case, the notion of Spanish right-to-colonize informed decisions by the Crown and by the Conquistadors, who often practiced brutal "pacification" on the local peoples.
The Spanish colonization of North America was less brutal than their efforts in Mexico and South America; because of the latter's artistic use of gold and their warmer climates, Spain took a greater interest and essentially wiped out the indigenous Mayan, Aztec, and Incan peoples. Their interest was bolstered by gold, and also by the exotic resources only available in the new lands. In contrast, the resources of North America were not as apparent, and so Spain took less interest. Most expeditions were made possible by Spanish superiority in military technology, as well as their mastery of horses, which were unknown in the Americas. By showing their military might and spreading Christianity throughout the indigenous people, Spain set the stage for the later British colonization.
Before I answer this, I would like to take exception to one thing in the previous answer. The Spanish did not wipe out the Maya, the Aztec, and the Inca. They did defeat the Aztecs and Inca militarily, but they did not systematically kill the bulk of the people. Instead (as part of their "general pattern of settlement") they used the people as laborers in their encomiendasystem. As for the Mayans, their great civilization was long gone before the Spanish reached the Yucatan and so they should not be spoken of as a major Spanish conquest along the lines of the Inca and Aztec.
Looking at the Inca and the Aztec regions, the general pattern of Spanish conquest was to use the advantages mentioned above, but also to use native allies. The Spanish took advantage of the fact that the people who the Aztecs and Incas had subjugated tended to hate their overlords. The most famous example of this is their use of the Tlaxcalans as the bulk of their force against the Aztec.
Once they had conquered, the "general pattern of settlement" was to give pieces of land to various conquistadors and others who came later. These lands were essentially fiefs for the Spaniards, who were entitled to the labor of the Indians living on that land and who were supposed to care for the welfare of the Indians, both physical and spiritual.
This was the general pattern of conquest and settlement in areas such as what is now central Mexico and Peru.