I booked my son's appointment at the embassy a couple of weeks back for yesterday. Top tip: join the telegram alert group to find out when appointments are released if you're struggling to get one. I gave my boss a heads up that I would be booking an appointment at the embassy to register the little man and I wouldn't be able to book a day off ahead of time as they go so quickly.
Anyway, appointment booked and I gathered the required documents. I was able to download my university transcripts and email my high school to get a copy of my transcripts to prove required residency in the US.
We stayed at the travelodge in Twickenham, which was right next to the station and there was a car park around the corner that cost us £12.80 for 24 hours. The hotel cost £60 breakfast included, so not a bad deal, and it was about 25 minutes on the train Vauxhall and a 12 minute walk to the embassy. Once we found the right door and they finished scrutinizing my passport, we were quickly through security and onto the second floor.
Our number was called pretty quickly, documents handed over, and fees paid. After our fees were paid, we were called to the desk again. They wanted to know if I wanted to renew my expired passport while there. So I did, and went and got a photo from the photo booth and paid that fee. They also made a second copy of my deed poll for my passport application name change. Very nice/helpful of them.
A short while and a coffee later, we were called over to the private booth and we took the oath for the little man and signed all of his paperwork. The woman congratulated him (not that he understood any of it at 6 weeks old), and said he was a natural born citizen and could run for president one day. Then we went off to pay for the DX envelope. The whole process took just over an hour- very slick. Everyone was very polite and friendly. My wife commented that she had never been treated so well at the embassy. My response was we were doing citizen services, and not visa.