When woman surrogate a baby.How do they get pregnant and become a surrogate mother. Do they have sex to become surrogate or some other way? ?

Traditional. A traditional surrogacy (also known as partial, natural, or straight surrogacy) is one where the surrogate's egg is fertilised in vivo by the intended father's or a donor's sperm. Insemination of the surrogate can be either through natural or artificial insemination.

Alex, I'll take "some other way" for $200. 

The surrogate may be the mother or may just be carrying the child. In cases where they aren’t the mother, fertility clinics take eggs from the mother and sperm from the father to form embryos and then implant an embryo in the surrogate. Hopefully it is successful and the pregnancy begins. When the surrogate is the biological mother, they collect sperm from the father and artificially inseminate the surrogate. 

it's a threesome.....

If the surrogate is also the egg donor, IVI or IUI is usually used. If the would-be-mother wants to use her own eggs -or- another egg donor is selected, then the would-be parents create embryos via IVF, and the embryos are transferred into the surrogate's uterus for (hopeful) implantation.

Artificial insemination.  

That depends on if the surrogate is also the egg donor.  If the surrogate mother is also the egg donor, then artificial insemination would be done to put the father's sperm in her at the right time of her cycle.  This is usually done in a clinic.

If the surrogate mother is ONLY for the purpose of a working uterus and the mother and father hiring the surrogate mother are using their own egg and sperm, then the doctor would harvest eggs from the biological mother and the biological  father would give a sperm donation and the egg and sperm would be joined in a laboratory dish.  The fertilized egg would then be placed into the surrogate mother.  In this situation, the surrogate mother has no real biological connection to the child.  This is know as IVF or In vitro fertilization.  

Some other way...

Eggs are taken from the biological mother. Sperm is extracted thru IKSI (a needle withdraws sperm-rich fluid from the testicles) if a vasectomy has been done or thru masturbation if viable sperm can be ejaculated. The eggs are fertilized in vitro (literally "in glass", hence the name test tube baby) and implanted into the womb of the carrying woman, the surrogate. 

That can and does happen but usually it's artificial insemination. Performed at a clinic.