Setting up accounts
Create or select a Google Account.
Register an account, fill all the informations required. You will likely want this account to be the same for the Google Play Developer account as well as the AdMob account.
Be sure to read all the licensing terms as you go along, to know your rights, what you are allowed to publish and what you can't.
Getting your account banned will prevent you from registering another account and monetizing further games using AdMob, so be very careful and thoughtful while filling your informations and publishing your games as well.
All the terms and most of the accounts are available in your own language, so never hesitate to set the most appropriate language in your account settings.
Set up your Google Play Developer account
Register, pay the asked fee and fill all the informations required.
This is where you will enlist and publish your application for the Google Play store.
Like for the Google account, the pages (and terms of service) should be available in your language and filling all the informations asked is pretty straightforward.
Set up your AdMob account
Note: The screenshots might get out of date if ever Google chooses to modify its interface.
Try to keep to the idea of the tutorial rather than follow step by step if this happens.
As explained in the AdMob plugin manual article, go to www.admob.com and register your account (linking the Google account of your choice).
Create an AdSense account answering the informations asked in the AdSense form.
Create an AdWords account giving the required informations as previously for AdSense.
Those two accounts and informations polls should be on the same page.
If you already have an AdSense and or AdWords account when starting this, you might obtain different informations.
Be sure to read the AdMob policy and Terms and conditions.
This is no game, so check them fully. Check the box when you are done and agree with all the terms.
Your AdMob account can be banned if those are not followed, making it so that you no further can get payments, run campaigns and basically monetize your game through this service.
Main points are :
You can only have one AdSense account (so getting it banned means no more monetization through this mean)
No cheating by clicking your own links/ads (whether manually or an artificial way).
Encouraging clicks is prohibited (asking, offering retributions, etc...).
Using links/ads on a page/application that contains copyrighted materials you do not own the rights to is forbidden.
And far more (sometimes unexpected), be sure to read and understand the full policy and terms (links should appear in your language and specificities may apply according to your own country of billing).
Here are also some more rules specifically applying to advertisement with the service in video games : https://support.google.com/adsense/answer/1706015?ref_topic=1271509&vid=1-635790538896033383-2638835734