This stitch is useful, especially if you want to fill broad stems. The weaves come out beautifully making it an interesting stitch to do, especially with threads like perle cotton or silk. The curves take on easily, but not too sharp curves.

I will work between two parallel stitch lines.

basket_stitch_1      basket_stitch_2
Fig 1: Bring the needle out from A, go in through B and out through C, as shown. Points A and B are diagonal to each other, while B and C are at the same level.   Fig 2: Now, we do a diagonal stitch upwards. So,go in through D and come out through E. Note that E lies at a point between A and B, and at the same level as D. 
basket_stitch_3   basket_stitch_4
Fig 3: Now, we continue with doing diagonal stitches between the stitch lines, each one parallel to the earlier ones. So, take the needle in through F and out through G, as shown. E-F is parallel to A-B.   Fig 4: Then, we do an upward diagonal stitch G-B, taking out the needle through C. So, from now on, we revisit earlier stitch points when working upward diagonal stitches.
basket_stitch_5   basket_stitch_6
Fig 5: Follow this technique making upward and downward diagonal stitches woven into each other.   Fig 6: The final effect would be like this. You can space them out or even close them in to suit your convenience.