Welcome to SDN. There are several threads here which have excellent discussions on the topics you are interested in. Doing a search will give you the URLs, or simply load all the pages in the Rotations and Residencies and International Forums to look for them.
In a nutshell, there is NOTHING you can do to GUARANTEE a US residency. But there are things you can do to maximize your chances (in no special order):
1) do well on the USMLEs
2) have US LORs
3) have US clinical experience during your 4th/final year
4) have good grades
5) have US citizenship or a PR
6) choose a primary care or other non-competitive specialty
7) do research in the US, getting to know US faculty ahead of time
8) follow the NRMP and ECFMG guidelines, send things in on time, etc.
9) be active in your extracurriculars during medical school - be an interesting and involved person
Obviously you don't have to do all of the above to get a residency but each factor has its place in making you a more interesting candidate.
Applications for the US NRMP are usually due by November 1 of the year before you start residency. To complete the application you would submit your transcripts, a photo, your LORs, a personal statement, USMLE scores and a Dean's Letter to ECFMG. ECFMG in turn downloads the information to ERAS which disseminates the information to programs you've applied to on-line. There are some programs which have deadlines earlier than November 1 (but usually not much earlier than mid October) and some which are later.
To remain in the match after the Rank Order List day, you must have completed and passed all the exams toward your ECFMG certificate. This includes USMLE Steps 1 and 2, TOEFL and the CSA. Last year the deadline was extended to mid January to have the exams completed, but it is traditionally end of December. Because it is difficult to get CSA test dates in the fall, you should try and have all the exams done by the time you apply for programs, or at least scheduled. Do not apply without a Step 1 score - you cannot take the CSA until you have taken Step 2 but can delay Step 1 if you wish. Information about these tests and the ECFMG certification process is available at: http://www.ecfmg.org
The process is expensive - approx $600 for each USMLE Step, $100 for the TOEFL (might be more out of the US), $1200 for the CSA, $95 to apply to the NRMP, $75 to apply to ECFMG to serve as your Dean's office, $45 for ECFMG to accept your USMLE scores, $60 for 10 programs through ERAS (you will most likely want to apply to more than 10 programs at which point the cost rises up to $25 per program after 20 programs I think), etc. There are fees everywhere - be prepared and you will of course, have to have money to travel to interviews as well. SOme hospitals will pay for your hotel, many will not.
Try and do some 4th year electives in the US; most schools have information on their web sites about visiting clerks and policies regarding IMGs. If you are interested in doing some in NY State, they require that you have an approval from the State Medical Board. The application costs $40 or so and requires that you have taken and passed USMLE Step 1 and have approval from them. Illinois is much easier - simply apply directly to the schools.
For more information:
(list of US residency programs)
(US residency matching program)
(info about the exams)
(info about the certification process for entering into US residency training)
(info for state medical boards)
best of luck...