Yes, many new-hires were indeed 'family', being those with relatives already working for the RR. One reason for this is the nature of the job and the lifestyle. Odd hours, until recently no holidays off until you had many years of experience, seasonal layoffs for newhires, much time away from home, and no set schedule. Lots of divorces on the RR. Thus the retention rate is abysmal, half the guys the RR would train would quit within 6 months. So they figured people with family members on the RR may at least have a better since of the lifestyle demands. Nowadays railroads will send out hiring info to state job agencies, and even run ads in the paper. But they might do so one week, and then not again for 10 years.
Now to your actual question of how one trains to be an engineer. First you have to get hired by the RR. Background screening(no speeding tickets), psychological tests(don't answer yes when asked "Do you like to drive aggresively?"), and scare stories about how 'you'll spend Christmas in hotels and never see your kids grow up, so do you really want to do this?'. Once hired your sent to trainmen's school, 3-6 weeks plus of the basics(or some are required before hiring to attend a community college RR program, basically the same). Then you are assigned to ride along with crews for weeks or months to learn the territory and get hands on experiences as a brakeman or conductor. After a period(a few months to several years) of working as a brakeman or conductor in the yards and then on the road you may get a chance to bid on going to engineer school, all slots filled by seniority. That is 5 weeks of fairly intense training, followed by 6 months of riding with mentor engineers and gradually getting to run under their supervision in a variety of conditions. I believe then the student has to sit for certification.
Used to be that trainmen and engineers were separate crafts with separate unions and seniority, but nowadays the major RR's are forcing all trainmen to go to engineer's school. So the above sequence will vary from RR to RR, but that should give you an idea. You don't have to be a rocket scientist to be hired by the RR, but they try to look for people willing to take orders and meticulously follow a routine. Military background is a big plus. But in a pinch they also will hire some real nitwits. It just depends.