Well there's really 2 practical options into getting involved into a career like this. And no, you do not necessarily need a degree, but it's almost impossible to do so without one.
1. You can go the traditional route. Which would require someone to start their career in Investment Banking (this usually happens right out of undergrad), transition over to Private Equity, build relationships and contacts, build personal wealth, and then start principally investing with a group of individuals or just yourself. This is the simple way of explaining it, but there's a lot of things that are involved between each step. A lot of it is centered around the ability to properly and accurately determine company valuation, debt-to-repayment analysis, Leveraged Buyout analysis and expected return multiple (and/or ROI) analysis'. Usually it takes an entire career to get to this point. I'm 33 now, and started from the beginning back when I was 20 (the very first deals I did was helping Facebook acquire financing to purchase complimentary strategies. This eventually lead to them buying Instagram which I've helped them do as well as their IPO back in 2013). So, you can imagine this does take some time to develop.
2. This option is a little more straight forward, but requires the person to have their own wealth already established. They've made their money already from their primary wealth generation tool (career), and they begin to invest in companies themselves which they find from listings (Angels list, Pitchbook, Prequin, Yieldstreet, etc). Now, you can stop here, and just work on your own, but without the proper knowledge of evaluating these companies, you're almost investing blind. Usually, once you get to a certain net worth, you have managers that do this for you (of course with a fee attached). Or you grow big enough and build out an investment company yourself. Guys like Steve Nash, Kobe, KD has all done this. Nas does this as well (he invested early in Ring, as well as Shaq).