To become an FBI HRT (Hostage Rescue Team) operator, you will first need to qualify as an FBI Special Agent. This requires a 4-year degree and a solid background. Having prior law enforcement or military experience will help you achieve this (and will help you when you go to HRT selection too).
You will be away from home for a 21-week FBI Special Agent training academy. If you become an FBI Agent, and you prove yourself and have a strong background, you can put in for HRT selection. A lot of HRT operators have prior experience in military special operations (such as Marine Recon, Navy SEALs, Delta, Special Forces, Para-Rescue, etc...) or SWAT teams from police, sheriff, and state police agencies. A background in any of these can give you a leg up. HRT selection is 2-weeks long, and is also at Quantico.
If you make it onto the HRT, you will respond to call outs as they happen. You could be called out for a few hours or a couple weeks. It all really depends on how long it takes to achieve your mission. Outside of the call outs, you may be called away from your field office to go to HRT training, this can also last a weekend to a couple weeks.
While there is definitely time away from home on the FBI HRT, it's not like the military where you're deploying for a year overseas, you'll have plenty of at home time.