When should someone expect to start earning money on steemit?

There is no specific estimate for that. Some people will start earning money on steemit right after signing up. Some won't make any money at all even after months of being an active user. 

Whether you earn on Steemit is dependent upon many things such as how many connections you have, how you promote your posts and whether your posts get upvoted.

Even if you write a high quality article on Steemit, if no one notices it and no one upvotes it, you won't make any money. But if you consistently write high quality articles and increase your follower base, then you will most likely receive upvotes of around 10 cents to 1$ sometimes. 

Also, you can increase your earning on Steem by contributing in platforms such as Utopian, Musing and busy.org. 

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There are lot of factors that affect / increase your earnings on Steemit. 

i) First of all, of course, Steem Power. If you have Steem power, say, 1000 + SP, you can earn by selling votes. 

ii) You can also earn by delegating your steem power through minnowbooster, and you will get Steem daily. If you are using this option, make sure that the delegatee has placed a lease request for a long time, not for a week or 2.

iii) Commenting on the posts of others may get you upvotes from them.

iv) Finally, you can earn by posting on Steemit, and with this option, you really need to produce quality content and also be a member of some communities that give upvote support.