The Arts and Crafts movement took off around the turn of the 20th century. Like the Art Nouveau movement, it developed as a backlash against the overwrought style of the Victorian era. It rejected the factory-produced furnishings and decorative accents that prevailed at the time, embracing instead natural beauty and traditional craftsmanship.
Some defining characteristics of Arts and Craft interior design are:

Colors from Nature
The classic Arts and Crafts palette takes its subtle, muted beauty straight from the natural world: stones, bark, leaves, grasses. Although you don't have to limit yourself to browns and greens, any hues that are less obviously organic, such as blue should be dusty or dirty.

Furnishings
Arts and Crafts style is as far from frothy Victorian sofas and ornately carved case goods as it's possible to go. Instead, it embraces sturdy, unadorned, comfortable furnishings that are built to last and are as much about function as form. What they lack in ornamentation, they make up for in the attention to detail and materials.
Most Arts and Crafts style furniture is heavy on the wood, but that doesn't mean you're doomed to an aching spine from hard chair seats. Simple leather, cotton or linen upholstery.

Natural Flooring
Arts and Crafts flooring falls right in step with the natural aesthetic: hardwood (planks or parquet), stone, slate. Tile with an Arts and Crafts glaze, a specially applied matte finish that lends tremendous depth, works beautifully in a mosaic grid. Cork is a great choice as well.
Choose a natural weave and don't get too ornate with the pattern, avoid flooring that looks too uniform, edgy or mass produced.

Lighting
Arts and Crafts puts less emphasis on accessorizing than some styles, and decorative flotsam is minimal. That means lighting, as one of the only real accents, needs to pop. Both mica and Tiffany (or Tiffany-inspired) glass lamps and fixtures fit the bill: mica for its organic feel and rich glow; Tiffany glass for the proud way it wears its craftsmanship.