How to start out as a music talent manager?

I would look in to a program at the Musicians Institute.
They have a music business degree available and they have all sorts of contacts. You will be able to intern in the industry and meet the people you need to know and learn how the business works.

A talent manager needs to know a lot about music, and have a lot of connections in the business.

I dated a guy who road managed and did talent mgmt. He started by learning sound board at a program (like a technical college)—because when you start out, you’ll likely be a jack-of-all-trades to some band as they build a following. (You will need to be the Road Manager, run sound, and manage the t-shirt sales cash box all at once. Really.)
Information on how to learn sound engineering / sound board skills here.

You’ll be told over and over that this is a very competitive job—a lot like people saying they want to be actors/actresses. LOTS of people want to do this job -not everyone can or will get the skills and then even fewer will luck into a position where they end up working with a band that gets major label support (read: $$) and/or a sizable fan-base. Until a band is signed or is making money (like Macklemore) you aren’t getting paid, or if you aren’t, it ain’t much. (Yes, really.)

The guy I dated totally lucked into working with a band that made it really big – which then led to him getting jobs to road manage other major label artists and then in addition he also talent managed some smaller acts that had potential (but never “made it”).
He got out of the business after about 15 yrs. because he was disillusioned with the alcohol/drugs & travel. He has since apprenticed to be a carpenter and teaches at a community college.

One last tip that I know my old BF tells all his students:
Unless you plan to never get married or have children (and you don’t really like to be at home or feel a great desire to live near to or frequently see your friends & family) this isn’t a job you can do for the rest of your life. It isn’t well-paying (except for the very few) and its a lot of sleep deprivation, cleaning up crap, hassle and hard work. My BF used to compare it to being a nanny to oversized children. The glamour of life on the road is stuff like finding a laundromat in every town..bringing the bus driver coffee, taping schedules to cheap hotel room mirrors that remind the band what time sound check is and trying to find a guitar tech on an emergency basis.

If you want to work in a major label (like manage artists for a major label—a bit more of a desk job) most people start out in college radio, then progress to professional radio, work their way up to Music Director and then some small few move to major labels. It’s entirely who you know and again, doesn’t pay well for a lonnng lonnng time. (I also worked in radio.)
Your best bet is to go to college (major in Communications), get active in running a college radio station, intern (unpaid work) for every major label or, if you’re really lucky, at MTV (I know someone who did this from my college station)..and if you make the right connections you might be able to get an entry level job at a label.