This is actually our 10th au pair, so we've had a wide variety of experiences. Some good. Some bad.
The cost and contractual obligations are easy. Agency fees are usually around $9000 for a year for a brand new au pair (it's cheaper if you extend). That covers them overseeing all aspects of the program, like background checks, facilitating contact, and organizing events for the au pairs. You pay the au pair $200 / week. I'd say our total costs are in the area of $21k / year. You also need to provide a private room for them. A real room. They can work up to 45 hours per week, 10 hours per day, no overnights and they need 36 consecutive hours where they are off per week (where "off" means they can walk out the door and be gone for those 36 hours). The contract is usually for a full year, but can be extended for an additional 6 to 12 months.
Usually our au pairs are responsible for getting the kids to school, picking them up, taking them to activities, and making sure homework gets done. This year will be...... different.
You can set up family rules. You should provide these before you match so there are no surprises (surprises are usually bad for both parties). Our rules are pretty simple; no drugs, no drunk driving, ask before you use the car, be well rested and ready to work, when you leave give us a vague idea of where you'll be and when you'll be back so we know when and which ditches to start looking in if you don't return. I'm happy to supply a redacted copy of our rules if you're that interested.
You don't need to supply things like a car or phone, but getting the best au pairs is competitive (I understand right now it's extremely competitive because nobody wants to, or can, come to the US). So we put together a kind of offer packet to make ourselves more appealing. We have a car dedicated for the au pair, but if they want to go more than 100 miles they need to pay for a service appointment. We provide a phone and a service plan. There's a community pool. And we pay for various memberships to amusement parks and museums so they have stuff to do (both with the kids and during their off time).
If things are going really bad you can go into rematch. Either the family or the au pair can trigger it, but once that's triggered the au pair has 2-3 weeks to find a new family or they are sent back. You as the family can take as long as you need, but you'll be without an au pair until you get someone. It usually takes at least 6 weeks to get a new person from out of country. It's hard for au pairs to find a rematch if they cause the rematch, especially given the short timeframe, so often they have to take a less desirable position.
We've gone into rematch twice. The first was with our very first au pair. She was really uninterested in the job because she was preoccupied with boy issues back home. The final straw with her was lying about causing a couple thousand dollars in damage to our car. The second one was at the beginning of this year. We got our first au pair from China and when she got here her English was significantly worse than when we interviewed her. The kids had a lot of trouble connecting with her, but we finally triggered rematch because she took a car she wasn't insured on out for coffee when nobody else was around. It was the third time she had done it, and after each of the first two we had someone who was a native Mandarin speaker explain to her that she couldn't take it. So in both cases the real issue was about trusting them.
We thought about going into rematch a third time. We had an au pair that was really good with the kids, but she was shockingly racist, bigoted, and fascist (she outright said people of certain races and certain religions should be executed, and when we compared it to the Spanish Inquisition she had never heard of it and then claimed that that was fake history and had never happened). It warranted a lot of discussion between us (the parents) and we decided to occasionally ask the kids if they heard her say anything like that to them. As long as she kept those opinions to herself around them it wasn't a problem, and it led to a lot of interesting discussions. Ultimately I think we softened her views.
We also had one au pair who ended our contract early. Our son has ADHD and he was just being diagnosed, so she had a really hard time with him. She decided she just didn't want to work with kids. She gave us a couple months notice which made it easy to get a replacement for her.
All in all it's been a very positive experience for us. The kids have had a wide variety of experiences with other cultures. Most of our au pairs have been European, so they've had Spanish, German, Austrian, French, and Polish influences. Our current one is our first male au pair (most agencies won't accept men), and he's been fantastic. He's from Brazil, so it's been an interesting new experience for the kids. My best friend married one of our au pairs (they were about 2 years apart in age) and moved to Austria with her. We stay in contact with most of them (even the rematches; our last rematch texted me last week asking for a couple of my recipes). We've also set up little vacation "franchises" around the world, and have traveled to Europe with the kids to visit ex-au pairs a couple times.
Happy to answer any more specific questions.