This varies from campaign to campaign for me.
It almost never starts with a map for me; in fact, I have played with the notion a couple times of having a truly medieval sense of space for the characters where the only map they have is of their (very!) local district -- everything else was vague for them.
My in-the-offing campaign began with the purchase of Monte Cook's AU and a lecture I heard about the Spanish conquest of the New World, how the Spanish took over the Aztecs and Inca through extremely lucky timing as much as anything else -- if they had arrived 20 years earlier or later, the situation might well have been very different, with much stiffer and more organized resistance. From there I worked up the societies, a couple of rough maps, did some reading on Mayan mythology and technology, Spanish colonization efforts, etc. In other words, this is a really intensely researched campaign, but most of the research will strictly be in the background, not particularly important to the characters, only to me as the GM. And I fully admit to this campaign being a bit over-the-top in that department!
One other campaign I had began with my sig line. I had a dream about people going into a hall and seeing a group of statues, very realistically carved, but with smooth ovals for faces. This led to a very creepy fantasty-horror mini-campaign where a group of necromancers had severed the connections between the people in long valley and their gods; the PCs were all locals who knew something was wrong, even though the land had been like this for a generation or more. I created a general map, several "set piece" adventure ideas, and a rough timeline of events-to-come. I also edited spell lists and the like.
The point though is that while my campaigns sound pretty intense in the R&D department, this is because I have been a GM since Day 1 of my gaming, since 1975/6. I have worked in grander and grander scope each time, as far as background material that I must at least develop for myself.
BUT a starting GM doesn't need to do nearly so much. Maybe you want a campaign to focuse on dragon-slaying. Fine. Come up with a reason for why they should be killed off, a rough map, and suggestions to the players on what kinds of characters would be most useful. If you want political intrigue, name a few nobles and start from there. There are many ways, in other words, to start designing a campaign; it is mainly a matter of taste.
You don't need a PhD to design a campaign; I don't have one and it never stopped me.

All you really need is love for the game, a fun idea, and a group of willing vict ... errr ... players
