It depends on the campaign. I have run one shots, mini-campaigns, and campaigns that have lasted up to 2 1/2 years (my current campaign will end near the 3 year mark later this year).
Generally, for mini-campaigns, I plan an overarching story arc, let the players know enough about it to build appropriate characters, and as play goes on I will add in side missions or the like depending on the characters and what they are doing, and tailor the story to the characters.
For normal campaigns (i.e. those that I don't plan a set end for), I plan a story arc or three for the early levels, throw out some information about the world, and see what the PCs do. As the campaign continues, I start weaving threads from the early days into later adventures and call that the overarching plot. Those threads extend out and become longer as the PCs spend more time working on them.
Generally, for mini-campaigns, I plan an overarching story arc, let the players know enough about it to build appropriate characters, and as play goes on I will add in side missions or the like depending on the characters and what they are doing, and tailor the story to the characters.
For normal campaigns (i.e. those that I don't plan a set end for), I plan a story arc or three for the early levels, throw out some information about the world, and see what the PCs do. As the campaign continues, I start weaving threads from the early days into later adventures and call that the overarching plot. Those threads extend out and become longer as the PCs spend more time working on them.