I too am living in Dallas at the moment, and I applied to a UK university during high school (Univ of Manchester to be exact) and managed to get in. I was set on attending university in the United Kingdom, and was...
nicely discouraged(?) for having "such high standards" by my fellow peers. For most of senior year, I didn't mention my wishes to go abroad very much. I understood their concerns and it's quite funny to see the looks on people's faces when I admit that I only applied to two schools, one in US (out of state) and one in the UK.
What are you interested in studying? Many degrees are only three years versus four years in the US, except in Scotland (four years). Just look up the prospectus on the university's website and it will list whether your degree is three or four years.
Get familiar with UCAS, it is sort of like the Common App in the US. You register on the site, they'll give you a username and an application to fill out. You'll have to write a personal statement saying why you want to study your subject and this will get sent to up to five degrees you choose. Keep this in mind, five
degrees and not necessarily five schools. For example, if you interested in a degree at Oxford in either politics or agriculture, you would need to take up two choices on your application. A major difference between how you apply to universities in the UK versus US is that you apply for your "major" instead of applying directly to the university and then deciding your major. Also UCAS is much cheaper, I believe I paid about 17 pounds to send the application to my five choices.
Take AP exams if possible and try to earn a score of at least 4 out of 5. They like it if you have about 2-3 exams with a score of 4 or 5. They are aware that final scores don't come out until summer, so if you inform them or show on your transcript that you are enrolled in the AP classes and intend to take the exam, they will give you a conditional offer, and decide whether or not to accept you based on your scores. All UK universities have a international students page that will list academic requirements for different countries, and US is always on there somewhere.
Offers. After you send off your application, you will wait for the universities to reply to your application. They can reject you, give you an unconditional offer or a conditional offer. An unconditional means that they are willing and ready to offer you a place at their school. A conditional offer means that they are interested in you, but want to see your end of year scores (like a 3.3 GPA) or AP scores, etc in order to make their final decision. They will inform you what scores they are waiting for in their reply. The hardest thing about receiving conditional offers are the conflicting dates for American deadlines. For example, imagine if you were deciding between a spot at an American university and one conditional offer in the UK. Most US universities require that you accept or reject their spots by May and if the UK university was waiting for your AP scores, which again, come out in summer, you would have a dilemma.
Documentation and advisers. I have found UK universities favor faxing versus mail post. As most (if not all) US universities require that transcripts be sent in a sealed envelope, the UK universities didn't care if they were open and sent through fax. Being in high school, new to the college application process, and also taking on learning how to apply to UK university was difficult. My advisers did their best to assist me, but as far as I know, I was their first student to apply directly to a foreign university. I don't know about your advisers or school, but be warned they might be new to the process too.
Everyone else around you will also be new to the process. Many of my friends thought my trying to apply directly abroad was brilliant and others...were less than encouraging. You need to determine for yourself if it is worth it. No one here on the forum or in your life can make that decision for you. At first glance, attending a UK school can seem expensive. But depending on where you are interested in attending in the US, it can be cheaper. Univ of Manchester (and the exchange rate was worse then) was significantly cheaper than my out-of-state US school. Univ of Manchester definitely would have been cheaper, tuition-wise, because I would have had to pay for three years instead of four. If you're deciding between a UK school and a state school, then going to school in the US would be cheaper. You have to calculate it out for yourself.
Visa. You will need a visa since you will be studying for long term. Currently student visa costs 145 pounds, which is actually cheap compared to what other UK visas cost. In order to be accepted for your visa, you need to be accepted by your UK university, show that you can pay for your first year's of tuition, and living expenses. If your school is in London, you would need to show that you have 7200 pounds or 800 pounds per month for nine months to live off of. Else where in the UK is 5400 pounds for nine months. You will be able to work a total of 20 hours per week on a student visa during the school semester and be able to work full time during school holidays.
Most likely, I have only found one university that doesn't do this, you will start your course in September or October. Again, I have found only one university that offers starts in the Spring. The UK system is in years instead of semester in the US. So you can't take off a semester here or there unfortunately.
Keep in mind that you will far away from home in a different time zone. Living is different from visiting. You will be immersed in a new culture that you will either grow to love or hate. It will be difficult when you first arrive, but if you stick through it, you'll meet new people, see new places, make new friends, etc. The experience, or any college experience you have on any continent will be what you make of it.
Also, if you ultimately decide to attend a US school, keep in mind that you can earn your master's in the UK. Most degrees only a year (15 months?) instead of two years in the US. If you are curious about this option,
tons of people on this forum have explored that option and are more than happy to give you their testimony.
Phew, I hadn't expected to babble on and on, but I hope it was helpful. I hope it all works out for you and good luck with your applications

Resources:
http://www.timesonline.co.uk/tol/life_and_style/education/good_university_guide/ This website gives university rankings
http://ucas.com/ The UCAS application
http://www.thestudentroom.co.uk/ Student forums
If you choose to end up in London:
http://moving2london.com/ Videos geared for Australians who wish to move to London, but tons of relevant information about moving to the UK in general
http://citywoop.com/ Two minute videos about different areas in London