First i would ask, what appeals to you. What would you enjoy watching most? Mountain stages? Stage races? Classics? GT's? ITT's? Maybe even cyclocross? If you have no idea yet, you could go on youtube and search for the most "spectacular races" etc. It's easier to get into cycling, watching a fascinating race, than it is following a seemingly boring ITT (personally, i love watching ITT's but not many do).
Then you need to see what your options are in terms of watching. If you are living in Europe, that will be a lot easier than if you're living in the US, Asia or Australia... There are a few topics about watching races if you live in the US, and what your options are. There are always options that are not legal, as Yaco pointed out, regardless of your location.
Next, like Potomac mentioned, check which upcoming races will fit your preference. If none are around the corner, you could start watching some old videos on youtube of previous editions of those races.
You might want to get acquainted with some of the different types of riders. A classics rider will not ride for a classification in a Grand Tour. A sprinter might not get over a hill and get dropped before the finish. A lightweight rider will not easily win a cobbled classic, but he will probably be a good climber and might win the classification in a stagerace or GT. Then you could also look for which riders fit that mold that might appeal to you more. Then look into what age they have, if they are in the peak of their career, or are they over the hill but carry a lot of experience, or are they inexperienced young riders who might do goofy (but interesting to watch) things.
There are countless of riders with unique abilities that might be one of a few favorites on a certain course or race, but who would have no chance on a different course. As such, there are maybe a hundred or more interesting riders to follow. It's easier to get into cycling if you can pick a few guys to cheer for, based on what i just wrote. But don't expect your climber of choice to feature in a drag race sprint.
Some of the most interesting riders to look out for (imho):
Julian Alaphilippe: One of the most versatile and successful road talents of the past 3 years. Excels in steep short finishes but very good at most other things.
Thomas De Gendt: wackjob of a rider, once on the podium of the Giro d'Italia, but known for his impossible breakaway attempts, and attacks from far. Amazing when successful. Usually rides stage races for stage victory, not for general classifications.
Tom Dumoulin: Timetrial specialist turned climber/GT winner. He speaks his mind and is a bit of a grouch. Makes him human and interesting.
Remco Evenepoel: Kid that was playing football 3 years ago, moved to cycling and obliterated the junior ranks. Turned pro immediately and started winning big races at 19 years old. Timetrial specialist and lightweight (so also good at climbing). Worst sprinter in the pro peloton. Also often goes for long range attacks.
Egan Bernal: easy lovable Colombian class act. Pretty much the only rider of Ineos (team) i can cheer for. Won the TDF 2019 at 22 of age.
Wout van Aert: the only rider able to oppose Mathieu van der Poel in cyclocross, turned into a worldclass classics rider and ITT'er on the road. Forever stigmatized by the mark of the underdog... eventhough he is a winner at heart (3x CX world champion, winning big races on the road in '19).
Mathieu van der Poel: Also 3x CX world champion, winner of Amstel '19, multitalent also successful in mountainbike. Puncheur, rouleur, sprinter... a bit of everything.
Peter Sagan: Multitalent. Comparable to van der Poel in skillset but 5 years older. Punchy classics rider and pseudo sprinter. Goofball first and foremost. Also 3x world champion on the road.
Tadej Pogacar: Slovenian rocket, 21 y.o. climber for GC. Packs a lot of punch and one of the youngsters to look out for.
Tom Pidcock: Main British up & coming talent, after a fading golden generation (Froome, Thomas, Wiggins...). Succesful as an U23 rider in cyclocross, cobbled classics, climbing stages, timetrialing...
And then there are others: Roglic, Valverde, Fuglsang, Higuita, Lopez, Yates (S.), Froome, Thomas, Pinot, Bardet, Van Avermaet, Lutsenko, Quintana, Mollema, Lopez...