Welcome to pixel art, one of the hardest artistic mediums there are out there, in my opinion. Also one of the most under-appreciated.
It's all about patience and lots of practice, if you want something at least decent.
Pretty complex medium too, lots of techniques to learn, quite the bumpy road too.
Here's some useful resources to get you started. All you need is any simple program like MS Paint, opaque pencil tool, magnifier, and that's pretty much it. [link]
I prefer to use mouse pads myself when pixelling, instead of a tablet, for precise pixel placement reasons, and Graphics Gale for the interface and right mouse click color picker. Point is, go and experiment, make your own rules.
Thanks for the replies guys! My main concern was that, while characters are small (they fit in a 50x50 box), it looks different to more traditional examples of pixel art characters. Specifically, the work looks sfumato, like an oil painting, with smooth transitions. I was wondering if that was most likely done pixel-by-pixel or using photoshop brushes with increasing levels of opacity
Yeah, it's pixel art. You can place the pixels individually if that's your thing. It doesn't exactly require amazing digital skills or powerful tools. You do, however, need to have an understanding of light, shadow and colour theory to know what colour pixel you need in that exact spot.
Here's a page of tutorials to get your artist started: [link]