This is going to be a huge and somewhat tangled answer so bear with me.
How do you begin in the roleplay world? Well, it depends a little on where you’re starting, i.e. tumblr, email, tabletop, mmo, forum, lj, etc. I’ve done all of those. But basically, the first thing to do is shape a character. Around tumblr those are often called ‘muses’.
You might feel a particular connection to a pre-existing character, a canon character from a book, a movie, a tv show, a game, a comic. Do you feel like you know a lot about that character, how they think and react? It might be a good character to roleplay. If you feel that way about a character with multiple canons, i.e. both book and movie, or game and comic, or in some cases play and book and movie and radio play and game and … you get the picture — you probably want to choose one canon to stick with.
Playing a canon character means you already have a worldspace, appearance, personality, and history to work with, but you probably also have ideas about that character that don’t clearly appear in their canon. Those are called headcanon, and as a roleplayer they’re hugely important — they help you shape that version of the character as your own, and separate you from all the other people also rping that character.
You might be more like me, slightly uncomfortable with getting into the mind of a pre-existing character. In that case, you have more work to do. You need to know what they look like. What gender they are, and what gender they’re into, or not into. Age. History, personality. Little things like the things they like and the books they read. You might not figure some of these things out immediately; they may come to you later, as you roleplay with particular people. This is particularly true of relationships.
After you have shaped your character, then you get to figure out how you want to get yourself noticed. That’s where all those things I reblogged can come in handy — along with following people, on tumblr. Simply following certain other players can often get you noticed, though not all roleplayers do starters (the ‘hi I see you followed me here is my muse noticing yours’ posts, which I don’t do). Or you can look out for exactly the kind of post I reblogged, and respond to them with the appropriate symbols in the other player’s inbox. Or you can just jump into someone’s inbox in-character (ic) and just play, or out-of-character (ooc) and plot.
Plotting can be complex, and this is where it’s especially important to both know your muse’s history and the other muse’s story — if you are offering to play with someone who is a singleverse player (everything happens in the same timeline), you’ll have to deal with not only your interactions with that muse, but be aware of any other interactions as well. My gadgeteerphilanthropist is singleverse. Other players are multiverse, meaning every time that muse interacts with someone new, it’s in a whole new timeline and space, as if no one else is interacting with them. This can present a much wider range of possibilities. Many muses combine the two, with a mainverse which is considered their primary plotline, and which new characters are most frequently placed in, and splits into alternate universes (AUs) for ideas or muses they find intriguing but which do not mesh with the mainverse. This is what I do — the Gadgetverse is my mainverse, but duplicate muses usually end up in their own AUs.
There are a few things which are specific to tumblr roleplaying. You should check out the differences between a primary blog (the one you log in to), and a secondary blog. The former can follow, and send asks; the latter cannot. It can be much harder to get noticed as a secondary blog.
There are a huge number of little tips and tricks with regard to roleplaying, especially on tumblr. Things such as cutting threads, reblogging photos as part of a roleplay, paragraph play versus conversation play versus gif play versus ask play. Patience with regard to replies. Many of these are things best picked up by doing.