The specific process differs by employer. This answer is marked wiki so anyone can expand the answer.
Finding a job
There are a few ways to find a job. Go do a job search on a jobs website (like dice.com). You can create a professional profile that describes your experience (such as on linkedin), and join groups on such website where they list jobs. You can contact a recruiter. You can go to the website of the company where you want to work and figure out how to apply. You can contact contacts in your professional network and ask if they know of anything. You can contact the school from which you graduated and see if they have a job search/placement program.
If you contact a recruiter, be aware of how they work. Do you pay them or does the hiring company? What happens if you find a job and apply to it, then they tell you about it? Do they require an exclusive deal? Do they focus on a particular region or a particular field? Are they okay if you use a different recruiter for a different region or field? What does the other recruiter/contract say? Will they modify your resume (they should never do this without your express approval).
Showing willingness to relocate
If the job requires relocation, you'll want to be sure that you point out your willingness to relocate. Some jobs allow people to work remotely, so relocation may not be required. You'll need to work out the specific details with your prospective employer.
The Interview Process
Recruiters like to interview you before sending your resume around. Good ones will stay in touch with you and prep you for the interview - tell you about positions they found and what the hiring manager is looking for. They'll ask you how the interview went after it's done, and they'll give you feedback from the hiring manager so you have greater success next time.
The hiring company may want to do a phone interview first. They may want to do two. Sometimes three. These interviews may take 1 to 3 hours, depending upon the company and who you speak to. They'll often want to do an in-person interview, either at an office near you with people who are qualified to interview you, or by flying someone to you, or by flying you out to meet them. If they fly you out, you may expect a per diem payment to cover food and incidentals, and they'll pay for the flight.
If they like you but you're not right for the particular position, you may be internally referred within the company and go through the interview process all over again.
Crossing State Borders
Travel between the states has no special regulations, but you should be aware that there are a lot of laws that change. For example, in CA, you have a right to work and a non-compete clause is unenforceable, but it's probably enforceable in the rest of the US. In the different states, the traffic laws are a little different, so you should familiarize yourself with the local traffic laws. Same thing for hunting, fishing, and some other activities.