Could a layman build a house from plans?
I used to have a teacher that said 


  Anyone can do anything given enough time and instruction.


That being said every trade has a learning curve to acquire the skills and required tools to accomplish the task.

I am a Master Electrician and have been in the construction industry for over 30 years. I am just finishing building a new house and here is what it have learned so far.

Some things are just not worth trying to do yourself.

So, here is what I hired out:


Excavation 
water well
septic
poured walls
concrete flatwork
windows and exterior doors 
siding
brickwork
garage doors
interior wall framing
basement stairway
drywall
air conditioning
ceramic tile
kitchen counters.


Here is what I have done / am doing myself or mostly myself with paid people to help me:


Framing
insulating
roofing
painting
concrete stain and seal
electrical
data
cableTV
security
smoke detectors
hot water heating
geothermal heat pump
solar water heater
photovoltaics
plumbing
interior doors
hardware
trim carpentry
kitchen cabinets.


I have been working in my spare time and paying out of pocket to avoid a large mortgage. It has taken me 6 years so far with about two more to go.

Sometimes I wish I had started this when I was much younger like yourself. On the other hand, I have acquired many more skills and patience in the last 20+ years that have helped me make this a great house.

Whatever you decide to do, understand that building even a small house is a complicated project and will require perseverance and patience. If you have ever spent a weekend doing a project then just multiply that by 1000 times or more, depending on the size of your house, and imagine how big a job this will be.

If you are still interested, then working in the construction industry for a few years first, will give you invaluable experience toward your goal.

Good luck!