Written test is your standard National Registry based type stuff. Pretty straight forward. Skills? Different areas may be different but when I went through my county's process there was no skills testing. The adjacent county does them (or used to in the past). Either way, again, straight forward and NR-based. You'd probably see airway/O2 (nasal cannula, NRB, OPA/NPA, suction), c-spine and a fairly simple assessment. If there's anything else, it may be traction splinting. Written and skills may be done on separate days or the same.
The interview is a panel of 2-4 people, usually 3. The questions are scripted and pretty basic. Not really any curve balls. Have answers planned and practiced. "Tell us about yourself" is always first and I guarantee few people are ready for this one. "Why do you want to work here?" (or some variation of that) will be another. Do some research on the company. Just poke around the AMR main site enough and you'll find plenty of factoids to use to say why you think they're so great. (I believe you can even find links to individual locations/operations which are useful). Again, I'd guarantee few people are ready for this and it'll set you apart. Also, have questions ready to ask them and make them company/job related. It shows you're prepared and interested.
Beyond that... dress up. Some people do the full suit, some don't. Really, the only difference is jacket or no jacket. Try to not show nervousness too much, speak clearly and avoid "um"s or awkward pauses, don't fidget, make eye contact with every person, shake hands before and after. Honestly, the process is pretty standard without any real surprises versus most other places. Don't let the AMR logo on the building freak you out.
**PS: This is just my personal view. Dress appropriately on the written/skills day(s). You don't need clean up like you would for an interview but close. Shoes, slacks, nice shirt (or nice polo at the least) and appropriate grooming. It's a competitive market (and industry as a whole) in terms of numbers so every little positive step to set yourself apart should be taken into account.