Moving here was actually very easy. These are the main things to be aware of:
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You have to register with the state within 14 days of moving into the country. In Zürich, this involves going to the Kreisbüro (district office) for the district you're living in, with your passport, proof of address and the contract for your new job. If you don't have an address of your own yet and are staying with somebody, they'll give you a form to get signed by that person and return. You pay them about 80 CHF (£54) and they will send off your application for residency, and give you a temporary Ausländerausweis (foreigner's ID card), to keep hold of while you wait. If you're from the UK and have a professional job here, you'll likely get what I have, the 5-year B Aufenthaltsbewilligung (more details here, though in German).
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Whenever you change address, you also have to go to the Kreisbüro and inform them. This also costs something, but not very much. The Kreisbüro people are generally very friendly and helpful, and speak English. More information here, in English.
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As a foreigner, your tax will be taken directly out of your pay packet the same as it is in the UK. This makes our lives easier than the Swiss, who have to pay their tax directly once a year.
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You must have health insurance, by law. You need accident insurance too, but your employer will arrange that for you. You can compare rates on Comparis and then sort everything out online. Insurance companies aren't allowed to turn you down for the basic insurance, but you will probably want to apply for extras to pay for dental work, etc. When I changed my insurance recently, I found they had a cheaper plan if you agreed to see your GP first for any medical issue, rather than charging off to make specialist appointments, i.e. what we're used to from the NHS.
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You'll need to get a Swiss bank account for your salary to go into. This is easy. It's best to go to a branch in person to do it, and bring your passport/Ausländerausweis/job contract. There are lots of banks to choose from, including the Post and the Zürich Cantonal Bank. It's common to have to pay a small monthly fee for a debit account, which is usually excused if you have a certain amount being paid into it per month.
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It's also easy to get a Swiss SIM card, whether pay-as-you-go or contract. NB you need to bring your passport when you go, because otherwise you might be A Terrorist.
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You need to get a Halbtax (half-fare public transport card). For this, bring your passport and a passport photo to the main railway station, where they also speak English. It currently costs 175 CHF (£118) for one year, less per year for a two- or three-year card, and 150 CHF/year (£102/year) for a Halbtax that's also a credit card, which might actually be a good deal but I refused it last time because I was so cross at their trying to upsell it to me. Once you have your Halbtax, the world is instantly a brighter and better place. You can also get a GA (general abonnement), which will give you all public transport free for one year, but it's only really worth it if you're commuting between cities for work.
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The biggest hassle we had in the move was transporting our stuff. We were very unhappy with Classic Moving and Storage, who took our money, magicked our stuff into limbo for five weeks and could not be arsed to answer any of our questions or apologise. Their subcontracters Luker Bros., however, were very professional. I wish we'd dealt with them directly.
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As for finding a flat in Zürich, that basically needs a full-length book of instructions and would still be nearly impossible. Once we manage to find a place bit enough to house David, David, me and a cat, I might post about it in more detail.
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Also, everything feels amazingly expensive at first, but you get used to that.
Points 1-7 can, or must, be sorted out when you get here, so don't worry about them yet. Let me know if you have any other questions about things I've missed out!