This whole chapter is reading out Dr Lanyon's letter.
It recounts how Lanyon got a letter from Jekyll asking him to break into Jekyll's laboratory to get chemicals to give to a man who would be collecting them
Lanyon's curiosity peaked and he went to meet this mysterious man. He noticed that it was a small, malformed man dressed in large clothes - this was clearly Hyde but as Lanyon had never met him, he didn't know
The mysterious man (Hyde) asked Lanyon if he should drink it elsewhere or drink it in front of him. As Lanyon had already been so involved in this process, he wanted to see the end
The man (Hyde) drank the potion and melted into Jekyll
This shook Lanyon to his core, resulting in his imminent death.