Applying for a cardiothoracic fellowship just requires that you contact programs with that fellowship for an application. Need to do it now though if you are heading into your PGY-3 year.
Our outgoing chief resident is going to Mass General for a combined cardiac and critical care fellowship that will allow him to finish in 1.5 years instead of 2 years. That one is somewhat competitive. Critical care in general though is not competitive and cardiothoracic is widely available.
Not all programs provide enough cardiac experience to their residents. I was contacted by a resident from a big and notable program in the north who was interested in transferring for his PGY-3 and 4 years because the program had to double and even triple up their residents in each pump case in order for them to make their minimum of 20 for the entire residency (only one resident is supposed to take credit for a CPB case with multiple residents involved).
In a program in Texas, if you do not make your numbers, the program allows you to code "extra patients" to get your numbers to acceptable/inflated levels.
In other words, it varies tremendously.
Having already done cardiac for my CA-2 year, I can tell you that it provides you with a unique skill set that makes almost all other types of cases seem routine (and even boring).
Be aggressive, stay late, and get as many cardiac cases as you can get. Even if you decide not to do them in private practice, the level of acuity of your patients, multiple procedures, and decision making skills you develop are absolutely indispensable for your future.