Taxes on wages from Appen Butler Hill

I wasn't really sure whether to post this here or somewhere like /r/personalfinance.

I've been doing some work for Appen Butler Hill for a few (maybe 3?) weeks now, earnings are about $300. My biggest concern is taxes - I've only lived in the US a couple of years and last month was the first time I had to file taxes (for 2015), so I'm still pretty clueless when it comes to taxes.

I know being an Independent Contractor it would count as self-employment. Am I correct in assuming I'd need to use Form 1040-ES next year, and that Appen will issue a 1099. Or do I use something else? I'm also concerned about the four payments I need to make during the year, how do I know how much to pay?

I'm a bit confused by all this, it feels like theres a lot of calculations and I don't want to make any mistakes and end up owing loads when it comes around to next tax time.