What are some of the Sioux Indians' religious practices?

The Sioux Nation (comprised of seven council fires and sub-tribes) had many spiritual practices. The foundational rituals or ceremonies are the seven rites:

The Keeping of the Soul (Nagi Gluhapi Na Nagi Gluxkapi)

The Rite of Purification or Sweat Lodge (Inipi)

Crying for a Vision or Vision Quest (Hanblecheyapi)

The Sun Dance (Wiwanyag Wachipi)

The Making of Relatives (Hunkapi)

Preparing for Womanhood or Puberty Rite (Ishna Ta Awi Cha Lowan)

Throwing of the Ball (Tapa Wanka Yap)

The Healing (Yuwipi)-- relatively new.

There are literally hundreds of other minor spiritual practices that the Sioux engage in...too many to mention here but you can find them in many fine books.