I will be traveling to London, have a basic phone and would like to know how to go about getting a SIM card - where and how. From what I've read, obtaining the card and loading time are different operations. I live in NYC.

Carphone Warehouse is a chain with branches all over the place and no tie to any particular phone service provider. If your phone's unlocked, you can get a card for a range of different providers and put some pay-as-you-go money on it (usually a minimum of £10). But there are plenty of other shops around selling cards on the same basis.

I have a cheap phone I bought in Asia and a UK sim card for which I'm billed on my credit card when I'm in the UK or Europe and using it. However, it's for the convenience and a pay-as-you-go sim will be cheaper per minute. They're available in supermarkets, as well as phone shops, Tesco likely being the biggest chain. Then, from previous experience, many little convenience shops wherever you go will be able to load more time for you as you need it.

Come to think of it, you could buy a (very basic) phone for not very much more than the initial card and top-up charge, so no need to worry about unlocking your "real" phone" or having that number unavailable.
phone-shop.tesco.com/pay-as-you-go-phones/
http://www.carphonewarehouse.com/mob...NOKIA_105/PPAY

I have an unlocked phone I bought for Europe but only used once. If I understand correctly, I buy the SIM card in one place and load time elsewhere. You don't buy the card already with time on it? Are all providers pretty much the same?

I have a pay-and-go card from Three; you buy the card with time and internet use loaded on. It's very simple, just put it in your phone, follow instructions and it is ready to use.
15 pounds gives you unlimited internet for a month and 300 minutes of calls, which I never use up.

There's a 10 pound card as well, that has limited internet.

Just find a Three store, they are everywhere. Other providers offer the same sort of thing, but Three is the one I use and am happy with.

AFAIK, all cards come with some time preloaded on to them, and you pay for both together, and then top up later as required.

If you're staying in and around London, and using the phone for calls within the UK, I wouldn't worry about the differences between providers. If you want to use it to make international calls, there might be some differences, and there are plenty of ads for specialist firms supposedly providing cheap international calls, but I have no idea whether there are major savings to be had over a fairly short period of limited use. That's one of the advantages of a seller not tied to one provider: tell them what your use is likely to be and you should get some idea of what differences there are, if any.

Have you googled "uk sim cards"? You can buy one in advance, have sent to you so you don't have to hunt one down on arrival.

I just had a look and even Amazon has them:
http://www.amazon.com/T-Mobile-T-Mob.../dp/B006H3575W

Even if they aren't the best deal in town it may be worth it for an easy short term solution.