What was the enlistment process like for the East India Company’s British soldiers?

I recently found I have a couple of ancestors who fought in India with the 108th foot regiment of the madras infantry. I’m not very knowledgeable on the East India Company and am a bit confused as to how British soldiers would end up serving a company on the other side of the world. I’m also interested in how their life would have differed from soldiers in the British army proper before they were merged. Thanks for any help.