It all starts with getting an FRN number from the FCC.
Here’s how to get one, direct from the FCC
You’ll need this FRN number to sit for an exam. New licensees must start by passing the Technician class exam. This primarily allows VHF and UHF privileges. For HF privileges you can upgrade to General class at any time after, including at the test session where you have passed your Technician exam. The final step is an Extra class license which gives you all frequency privileges available to US hams.
There is no longer any Morse code requirement. The exams are multiple-choice given by a Volunteer Examiner (VE). CARS has a VE Team and currently gives exams 4 times a year. The next exam will be noted on the home page of this website. At present there is no fee for the exams. The FCC does charge $30 for license issuance. Licenses are good for ten years and can be renewed.
Study resources are available at this page