There are quite a few blog posts and websites that talk about the process of getting an American Visa. Some of them are fairly full of doom and gloom, so I thought I'd give my much more positive take on it.
The DS-2019 is a document that your future employers have to generate before you can apply for a Visa.
This stage seemed to take the longest.
There was an on-line form I had to fill out first, I suspect that different universities/workplaces have different procedures at this point. I had to provide proof of medical insurance (provided by the department and an email seemed to count for this), a scan of my passport, my Phd certificate and a letter of invitation from the Dean. This whole process seemed a bit circular since the letter of invitation and the medical insurance were both coming from the department I had to send them to!
Once I'd fill the form out, it took 2 weeks for them to generate the form and fed-ex it to me.
When you get your DS-2019 there will be information included about how to go about paying your SEVIS fee. I don't really know what this one is for, but you have to do it. Make sure you have a credit/debit card handy and that your printer is connected. You'll need to print out the receipt to show them at the embassy.
DS-160 Nonimmigrant Visa Application Form
This is the form that allows you to apply to go for a visa interview. It is very long.
Things you need to make sure you have:
Your DS-2019, you can't apply without it
A US Visa style photo. This has to be square, so a UK passport photo won't do. You can get more info from here: http://travel.state.gov/visa/visaphotoreq/visaphotoreq_5334.html
Your SEVIS I-901
Keep printing out everything, particularly your 'instructions page'.
Apply for a Visa interview
This was pretty easy, choose a time and a day. They don't make you stick to your time, but I'd suggest an early one anyway. If you go early you don't get a backlog of people.
My interview was at 9.30 in London. I arrived at 8.20, there was already a queue, but only a small one. First you have to join the queue to say you're there. They'll check you don't have anything like a mobile phone/laptop/ipad/kindle etc. They'll also give you a plastic bag to put you watch and belt into for security. Try and only take in what you need, there is a pharmacy near by where you can store stuff, but I was lucky in that I could leave everything at someone's house. All I took was my debit card, my oyster card, the paperwork and a (hardcopy) book.
Once you've been checked in you join another queue. They'll check your paperwork again and then send you through to security. Security here is less scary than at the airport, and they don't make you take your shoes off.
Once inside, you'll be directed to a reception desk. Here they'll check your paperwork (sensing a pattern?) and give you a number (well it's a letter and a number, but you get the jist).
Now you just have to wait until your number is called. It'll blink up on the screen with the number window you have to go to. There are also hand instructions about exactly what you need to give them. They'll take everything off you. I felt quite naked sitting in the US embassy without my passport!
Then they'll send you back to wait to be called up again. The second time you're called is your actual Visa interview. I was asked what my job was and then she got me to explain what that meant. But it almost seemed like a friendly conversation. Also she enthused about Rutgers a bit. That was it. I was told I'd be given a Visa and that my documents would be returned in ~ 5 working days.
In all the visit to the embassy only took 45mins which wasn't bad considering some of the scare stories of waiting for 5 hours etc. that I heard!