Any video course that teaches you how to role-play?

[Pauly]

Seth Skorkowsky on Youtube has a number of videos on these points. I won't say I agree with him on everything but he generally has a mature and well reasoned approach.

[Psyren]

A while back, WotC put out a video series / playlist (https://www.youtube.com/watch?v=ZsPrUwcjxEw&list=PLfS8QgUdeGYr-v1QfBH4x_diAZ7SGNFj4) going through the basics of what the game is and how to play that includes a video on how to roleplay. (https://youtu.be/viJF5Risdnw?si=m_SjO-xy2SneSwyk) It's more D&D focused, but that's more or less how most people got into the TTRPG hobby anyway.

[KorvinStarmast]

Learn by doing.

[KillianHawkeye]

You're not going to have to do any improv or verbal roleplaying if you do PbP. You can take your time to type whatever you want.

[MoiMagnus]

Consider joining a theatre club (preferably an improvisation club, but even regular theatre should work) for one year. Most accept complete beginners, and all of them (at least all the good ones) should cover the very basics of roleplay:
(1) How to be confident enough to talk and say "silly things".
(2) How to be mindful of what the other peoples are doing and how they are reacting.
(3) How to react quickly and adapt to unexpected developments while remaining in character.
(4) How to immerse yourself in a character that isn't just "you but with slight changes".

Given that it's play-by-post, you might think that a writing group would be a better idea, but I think the core of roleplaying is in the interactions with others and as such theatre is more adequate.

[Slipjig]

B. Dave Walters has a class available for players and another for DMs. I haven't taken them, but I've really enjoyed his work in both capacities. If you enjoy his work, might be worth checking out.

But the right things for you to studying is going to be heavily dependent on what kind of games you want to play in/DM. For a free option, you might start with both Relics and Rarities and the first season of Dimension 20's Fantasy High, both available on YouTube. Both games had players who it was their first time playing DnD, so everything should be understandable to somebody just getting into the hobby.

[Vahnavoi]

As far as books go: old Basic D&D boxed sets and Middle-Earth boxed sets both had single player choose-your-own-adventure tutorials for how to play roleplaying games. More recently, Lamentations of the Flame Princess Grindhouse Edition boxed sets include a similar tutorials, taking direct cues from the Basic D&D boxes set. If you can't find any such thing on sale, check nearby libraries.

But in general: don't stress about playing all that much. A lot of different games can give you the basics. For kids, playing house with dolls is sufficient. The rest is learning game specific rules combined with trial and error, or as KorvinStarmast said, learning by doing.

As for game mastering: nearly every game comes with its own instructions for how to run it. So before considering any video course, pick a game and go through game specific material. Typically, you can at least try to hold a game based on the written rules.

But if you want to become good at running games in general, in person, join Scouts and maybe aim to go through Scout Leader training. Reasons why:

1) Scouting will give you real life perspective for various activities characters might try in a roleplaying game, from camping in the woods to climbing and sailing if opportunity allows.

2) A Scout Leader's course will teach you how to schedule and organize weekly group activities, which is one-to-one with organizing a roleplaying group or club.

3) Merit badges for Scouts include Acting & Drama, Literature etc., with ready-made teaching materials and instructions available for Scout Leaders.

4) Scouting activities also naturally incorporates all kinds of games, from children's games and physical sports to tabletop games. Roleplaying games can be included in that list and some countries have roleplaying games made by Scouts for Scouts available. Though really, the more important part is that being able to organize all kinds of games for kids will give you ideas for and helps you organize roleplaying games.

5) being part of an active Scout troop means you have a body of people to ask to play, and if one particular roleplaying game doesn't take, it doesn't have to be end of a group, because you have all the other scouting activities in common.

[Mastikator]

I second Seth Skorkowsky (https://www.youtube.com/@SSkorkowsky) and add Dungeon Masterpiece (https://www.youtube.com/@DungeonMasterpiece) as a resource for GMs.

Great Player Etiquette (https://www.youtube.com/watch?v=UiCxyBi8lRk) is a video I'd recommend for players. And this video about the Matt Mercer Effect (https://www.youtube.com/watch?v=vsYFEZNAAlo) is a great video and short video with some really good tips on how to make better combat, quests, social encounters and exploration.

[Tanarii]

Not videos, the top RPG blogs are worth reading. The Alexandrian, Hack & Slash, Angry GM.

And if you're interested in world building that looks anything like historical: ACOUP.
If you're interested in crazy adventure or campaign ideas loosely based on historical but with a super fantasy twist: Dungeonomics.

[Ozreth]

Buy the game, preferably a product with quick start rules.
Get 3-4 other friends together.
Play the game.
Adjust rules and expectations as the sessions go on.

Basically how its been done since 1974 and still the best way to do it. You don't need more than that. And don't put too much pressure on the acting/theatre/improv stuff. The expectation that your game looks like a theatre production is a result of some more recent D&D shows and podcasts that cropped up in the 5th edition craze and are not exemplary of how most people are playing around their home tables. This has been a problem as it makes the barrier to entry high for what is an otherwise simple gaming experience, and you end up with posts like these where people feel like they need courses to play the game.