Hi David!
How to apply:
No, you need not send your GPA and SAT scores in an envelope haha. All students applying to U.S. colleges make an account on either the Common Application (link: http://www.commonapp.org/) or Universal College Application (link: https://www.universalcollegeapp.com/). I think there were some more sites, but these two are most famous and work just fine. I am using the Common Application and would highly recommend it. The Common App allows you to apply to all of the colleges you like without making an account on each of their websites and filling in your information a trillion times, but rather only once. You need to register (make an account), select colleges (in the My Colleges section), fill in your personal information (in the Common App section) etc. On the Common App, you can also submit all of the essays required by the universities you will be applying to.
As for sending scores: as well as your essays and personal info, you send these in electronically. Well, how do you do this? You go to the site on which you registered for the test and log in (so, for the SAT, you go to collegeboard.org). There, you can look at your scores and will see/get the option ‘Send Scores’. From there on, you will either have to fill in codes that belong to the universities you will be applying to: these codes are to be found on their websites, likely on the ‘Application requirements’ page (for example, for Harvard: https://college.harvard.edu/admissions/application-process/application-requirements). After you have sent your scores (you can do this at any time you’d like, as long as they receive them before the application deadline), they open a folder with your name on it. To match your scores to your application, when you submit your application on the Common App, they use your personal info, so you don’t need to worry about how they’d match your scores to your application.
Way more information is available on their websites. Just google ‘[Insert university] application requirements undergraduate’ and you’ll find the page with ease.
Financial aid programs:
Multiple universities will meet your full demonstrated need, if admitted of course. For example, for Harvard, if your parents make 50,000$ per year and you don’t make much too, if anything at all, you and your parents are NOT expected to contribute (except for you with a job on campus) and the university will pay all of your fees. However, if your parents make 1,000,000$ per year, don’t expect to get any aid. To see what you’ll probably have to pay, check the Net Price Calculators on the websites of the universities you’ll be applying to. For example, for Harvard: https://college.harvard.edu/financial-aid/net-price-calculator.
Some universities, however, take your financial need into account when reviewing your application (like Stanford University), meaning your chances of admission get lower, because you need aid. But but but, if you get admitted, they will provide you will the aid you need. When they do not take your financial need into consideration, they have something called ‘need-blind admissions’, like Harvard, Yale, Princeton, MIT etc. If they do take it into consideration, they’re not need-blind, but need-aware, like Stanford, Columbia etc.
Chances of admission:
This is a tricky one. No one exactly knows. Of course, an International Science Olympiad medalist has a better chance than someone with a GPA of 2.0 and no awards/honors, but no one knows what exactly goes on in the committees. However, you can check their admission statistics. I love the ones Stanford publishes, because they’re pretty detailed (link: http://admission.stanford.edu/apply/selection/profile.html). Because you didn’t tell your SAT score, your EC (extracurricular activies), your exact GPA (a 3.8 >>>>>>>> 3.3), your awards etc etc, it’s impossible to tell if your chances are decent or awful, or somewhere in between.
Hopefully this could have been of any help. Good luck with your application!