Infectious disease fellow here. I'll break down the general roles of an ID pharmacist, although the experience may vary by institution.
Most are involved in antimicrobial stewardship, which variously involves setting up and overseeing antibiotic restriction policies, surveillance of antibiotic use (either on a continuous daily basis, or more intermittently through MUEs), working on antimicrobial monographs for P+T, building ID-related order sets, etc. These roles all require close coordination with infectious disease physicians, clinical microbiologists, and hospital infection control policies. Non-administrative-type roles of a stewardship pharmacist also include serving as a drug information resource for the pharmacy and infectious disease physicians. Again, these roles vary based on institution, and overlap with the clinical aspect.
The clinical roles of the ID pharmacist typically involve rounding with an ID service or other hospital service (the rounding responsibilities vary widely from place to place, not all ID pharmacists round). On rounds, responsibilities typically include drug dosage optimization, drug selection based on disease characteristics/microbiology, as well as provision of general drug knowledge about non-ID related drugs and their interactions. Depending on the service and the pharmacist, the pharmacist may have a role in diagnostics (interpreting rapid diagnostic tests, culture data, etc.). Other roles include outpatient management in HIV or general ID clinics, with some institutions having dedicated outpatient parenteral antimicrobial therapy pharmacists.
Getting into the training aspect - residency slots are somewhat competitive, as it is a popular pharmacy specialty with a limited number of residency slots. I wasn't in the match this last year, so I haven't checked the match rates, but they are available for your perusal. ID residency experience varies based on the institution, but you're generally exposed to all of the above listed experiences plus related fields (transplant, heme/onc, critical care), with some institutions having dedicated microbiology rotations for the residents to participate in.
I chose to pursue ID because I think its a hugely interesting field, with pharmacists in a great position to make an impact on a huge number of patients through stewardship and rounding. On a day to day basis, I see everything ranging from advanced AIDS to orthopedic device infections to stem cell transplants to well-managed primary care patients in an HIV clinic. Through stewardship, I get the chance to participate in the care of every patient in the hospital with numerous interventions made on a daily basis. As a fellow, I also have the ability to become involved in incredible research with the truly great minds in ID (pharmacist or physician). I don't regret the path I've taken for a minute.
If you have any other specific questions, let me know!