You can get the federal employers tax id number at the IRS site..
You should check your states web page to see about any state licences and such that you mite need.. like a resale tax number.
The Federal tax Id number is like your companies social security number.. Its also used when you have employees to keep track of the taxes you pay for that.. If You have no employees and run your business under your name.. and not a *DBA* This is not a requirement altho it is free to get and easy.. so it kinda nice to have just in case you need it... It is from the federal government.
The resale tax number is from the state.. and it is what you need to buy many things wholesale.. It makes it where you do not pay taxes on the things you are going to resell.. and It entitles you to collect taxes on the things that you sell.. You then pay the state the taxes you have collected from customers on the schedule they set up for you.. I pay quarterly.. (I hate writing that check)
What is the normal route to register a business?
Can I just register a LLC online and not have to go to my county?
You go to the county with a DBA, partership, etc. All others to the State. Now, your local government may want a license (read tax) and that will be your city or county or both.