No doubt the process is very different depending on your country, state, and perhaps even county? I'm in Europe (Poland) and I've built a house and a couple of buildings using online purchased plans and self-made plans(this is allowed for certain non-residential buildings up to certain size around here). I think it is quite interesting to compare similarities and differences in how it's done in other placed so let me briefly describe my experience.
First, the house. When I was buying the land, I made sure local council is fine with converting it from farmland to residential (the soil has to be pretty bad to allow it) and I got it in writing specifying certain general limits of what I can build there before I pulled the trigger on the purchase. Buying land that is not in much demand helps in this as there is no pressure on the buyer.
Then I went to a local website that sells house plans made up by certified architects and I bought one that I liked and it matched the council requirements (certain roof shape and color etc).
Then I had to hire a land surveyor to make a very detailed map of my land, and surrounding area, do research to discover any old underground systems and put it on the map etc. This map gets filled in a national database and any future neighbor will be able to use it for free, but me being the first to build around here I had to pay for it.
Then, with map in hand I had to hire an architect to "adjust the house plans to the site". The architect is supposed to take soil conditions, local site and everything else into account, they are supposed to redo any structural calculations and they sign the plan validity so if the house falls down they're on the hook. As you can imagine it costs more than the purchase cost of the plans online. But it still is much cheaper than custom drafted plans.
Then you go through the permit process which is really just a formality and you hire a company to build it or you hire a certified residential building manager directly and a different crew for each stage. At the end your land surveyor has to come over and certify you built the house where you should. The end.
Then the self-drawn-plan buildings. I wanted to build a workshop (of course). But I couldn't afford to go through the whole normal process again so I decided to limit it to 35sq meters (380sq ft). This way I didn't need any permits, no architect, no certified builder etc. I still would be bound by codes, but it is all on me.
I've drawn it myself. I looked up codes for the required roof slope (this being single slope roof). I looked up snow loads and wind loads. Calculation methods for timber thicknesses and spans. I already had the house plans I could use for reference as all the calculations were shown in there step by step(for concrete not wood, but still it showed me how it should be done). So I was fairly confident in that my workshop shouldn't fall down on my head.
So being short on cash I hired a crew that was very cheap, but never built a building before... I had to supervise them all the time, but in general I did get a nice wooden post beam constructed workshop out of it for less than half of the usual per unit area price.
So here you have two very different approaches to build on the same piece of land.