I have a British passport but my daughter who is 2 was born in South Africa. I am coming back to live in the UK and want to bring my daughter with me. How do I do this? What type of visa can I apply for once she is here?
The answer depends on the basis of your British citizenship. If you are a British citizen "otherwise than by descent" then your daughter is also a British citizen, and you should apply for a UK passport for her.
You are a British citizen otherwise than by descent if you were born in the UK or an overseas territory, if you were naturalized as a British citizen, or if you were born outside the UK and territories while your parent was abroad in "crown or similar service." Details are available at Children born outside the UK: British citizenship.
If you are a British citizen by descent, then your child is not a British citizen, but may be able to register as one, depending on your circumstances. For example, if you lived in the UK for a period of three years with no more than 270 days absence during that three-year period, and your father or mother was British, then your daughter qualifies for registration. This costs £1012. Details are available at Apply for citizenship if you have a British parent; You were born on or after 1 July 2006.
If your child is not eligible to register as a British citizen, depending on the circumstances of your child's father, she may be able to apply for indefinite leave to remain, which costs £2389 or £2999, depending on whether you apply in person. Details are available at Find out if you can apply to settle in the UK.
As you can see, this is a terribly complex matter, so if you were not born or naturalized in the UK, you may want to talk to an immigration lawyer.