it is straight forward.
The first thing that you do is to take your licence and medical certificate to a Flight standards district office, they are all over the US and a list is available on the FAA website.
The next thing that happens is that you fill out a form and the FAA give you a FAA private certificate based on your foreign licence(cost $0.00), this certificate is only valid as long as your foreign licence remains so.
next go and get an FAA medical
the next thing you do is to do the written and checkrides for any other rating you have for instance commercial multi-instrument.
There is no requirement for formal training just a signoff from your instructor, however much flying you have to do to be ready for the checkride is between you and the instructor.
Once you pass the checkride then your certificate becomes free standing (ie even if your foreign licence expires your FAA stays valid)
One final note you will not be able to do part 141 courses as they are approved and in order to qualify you would have to follow the entire syallabus including all the flying hours so it would not be finacially wise to do a part 141 course but the FAA will allow you to qualify under part 61.