Of course, in order to actually come to the UK from the US, you need to make sure you have a current passport and a visa. I renewed my passport and then applied for my visa over the summer prior to moving here and had no problems. Read the documentation and follow the instructions on these websites:
Better people than I have explained that process in depth, so I will not go into it. Suffice it to say that if you don't have both of those items, you will be turned away at Customs (and possibly arrested, deported and humiliated).
If you're going to stay for any length of time, you will need a bank account, a phone, and some form of transportation. In fact, without these things, flat hunting will be very difficult, so you may want to take care of these things as early as possible.
There are a number of different banks here in the UK and some have branches in the US. If you have an account with one of these banks (Barclays, HSBC and Lloyds come to mind), then it is possible you can easily transfer to a UK branch--I really don't know; talk to your bank. My expectation is that nothing in banking is easy, so there is probably some hidden catch or it will involve hours on hold with customer service. Or both.
If you choose to wait until you have arrived to open an account, you shouldn't have too many problems. As with most other official functions, you will need to show your passport and often, something that explains why you are in the UK. This might be a letter of introduction from your university or employer. Some banks require this, others don't. Do your research.
Transferring money from the US to the UK is a pain. Not only is there the conversion rate (roughly $1.60 to the £ at this writing) but you can't simply write a check from your US bank, you need to do an electronic transfer of some sort. depending on your US bank they may or may not charge for this, but will probably charge around $60.00 per transfer. In addition, there may be conversion fees, bank fees, and other miscellaneous fees that will make your seemingly substantial deposit diminish before your eyes.
Another option is to use a Western Union wire transfer. This will cost $50.00 for up to $10,000 but may still be subject to other fees. Often, these will be less than letting your bank handle it, though. The major drawback of Western Union is that you need to pick up the cash and bring it to your UK bank. This may not seem like a problem, but not all Western Union offices can handle large amounts of cash. It can quickly become uncomfortable when you're carrying £5000 in £20 bills through a dodgy part of town.
Once you have some money in your bank account, then all is well. You are now able to start paying your long term bills like rent, power, telly and so forth. Most of these things can actually be paid online, and most companies would prefer that you set up an automatic payment when you start the service.
In the UK, cell phones are commonly called mobiles. If you already have a mobile, you can probably get a pay-as-you-go SIM only plan. This only requires you to swap out your old SIM card for a new one, unless your phone is locked. In that case, you need to contact your US wireless service and convince them that you are worthy of having your phone unlocked. If you are out of contract with ATT, for instance, then they will barely resist your request. If your phone is still under contract, then they may require you to pay a penalty.
Once you get that sorted out, you can go to one of the many mobile phone dealers and get yourself a plan (and a new phone if necessary). Shops like Carphone Warehouse are sprinkled up and down Princes Street (The main shopping district in downtown Edinburgh) as well as in malls throughout the city. The staff will hopefully listen to your needs and get you the best plan available.
Edinburgh and many other UK and European cities have excellent public transportation. I find that they are also very easy to get around on afoot. In Edinburgh, the bus system (lothianbuses.com) seems to be very reliable and runs all over the city. There are several rail stations where you can catch a train to another city, as well as an airport where you can fly virtually anywhere.
Unless you are currently a hard-core biker with experience in big city biking, I would not suggest leaping onto a bike right when you get here. Things are likely to be a bit disorienting, and the fact that they drive on the left is just one of many adjustments you'll need to make. Wait a bit until you're used to the traffic patterns and maybe get hooked up with other bikers before venturing onto the roads on a bicycle.
Buses currently cost £1.40 for a one-way adult single or £3.50 for am adult day-ticket. You need the exact amount when you get on, since the driver cannot make change. Just drop your coins into the fare box, tell the driver what kind of ticket you want (i.e. Adult Single), and he will generate your fare. A paper ticket will then pop out of a printer near the driver (either next to the fare box or behind him in the corridor). Take your ticket and find a seat.
Seating on the bus is variable depending on the time of day, but here's what I've observed is most common:
Front of the bus: Reserved for the elderly, infirm or handicapped. Often taken by tourists who don't read the "Priority Seating' signs, and by people who just don't care.The upper floor of the bus on the double-deckers is often divided similarly, save that the front is full of tourists, usually with cameras.
Middle of the bus: Here you will find the people who are on the bus simply for transportation, going to/from work, uni, shopping, etc.
Rear of the bus: This is where the dodgy people sit. Schoolchildren and teenagers mostly, who seem to think that they are on the party bus and by sitting in the back, the driver won't stop them from being rowdy. Which is true. They usually come aboard and disembark in packs.
Walking is another great way to get around Edinburgh, especially after you have a phone with a mapping program on it. You can easily walk from the City Centre to the Ocean Terminal in Leith if you are reasonably fit and have the time. It's about a three mile journey, and you pass some wonderful shops and buildings along the way. If you're planning on simply hanging around the City Centre where Edinburgh University, the castle, the museums and the main shopping district is, then plan on walking. Everything is within walking distance, usually just a matter of a few blocks.
I think I've gotten this blog up to date on the how-to aspect of getting to Edinburgh. With luck, my next entries will deal more with the city itself and my own experiences.