It's my first time attempting a speed run ever

Think I have livesplit set up so what do I need to do next? How do I apply the livesplit in the speedrun is this done with Twitch?

You would need a streaming software and a capture card (assuming you're playing the game on PS4) to be able to do that. But, to be sure, what version are you planning to do? If it's PS4, if you have a decent connection, you can use Remote Play on PC and use your streaming software to capture the footage with livesplit (I recommend OBS for that, as that also requires a different setup). Have you made sure the load remover is working? Because it has been updated to revolve around the recent change with loading times.