Gamete Intrafallopian Transfer (GIFT) is an assisted reproductive technique were the eggs are retrieved from the ovaries just like an IVF procedure. Then the Gametes (Eggs and Sperms) are placed into Fallopian tube with a help of a catheter using a surgical procedure called laparoscopy(as shown in the figure below) where the egg gets fertilized.
Zygote Intrafallopian Transfer (ZIFT) is an assisted reproductive technique were the eggs are retrieved from the ovaries just like an IVF procedure. These retrieved eggs are then mixed with sperms in the laboratory. Then the fertilized eggs (zygotes) are placed into fallopian tube with a help of a catheter using a surgical procedure called laparoscopy(as shown in the figure below). The zygote should eventually be implanted in the uterus and develop into a fetus. 
In vitro fertilization is an assisted reproductive technique were the male sperms and the female eggs are fertilized in a laboratory. The fertilized egg is developed into embryo stage which is then placed into the woman’s uterus with a help of a catheter.
Hormones control the human body’s reproductive system. The two hormones secreted by the pituitary glands are follicle-stimulating hormone (FSH) and luteinizing hormone (LH), both of which are secreted in response to the release of GnRH from the hypothalamus. FSH travels to the ovaries and stimulates a group of follicles to grow. These primordial follicles develop into primary follicles and then secondary follicles.
Follicle stimulating hormone (FSH) is one of the gonadotrophic hormones. FSH is one of the hormones essential to pubertal development and the function of women’s ovaries and men’s testes. In women, this hormone stimulates the growth of ovarian follicles in the ovary before the release of an egg from one follicle at ovulation.
Luteinizing hormone (LH) is produced and released in the anterior pituitary gland. It controls the function of ovaries in females. Two weeks into a woman’s cycle, a surge in luteinizing hormone causes the ovaries to release an egg during ovulation. If fertilization occurs, luteinizing hormone will stimulate the corpus luteum, which produces progesterone to sustain the pregnancy.
During the time of puberty in females, out of 60,000 to 80,000 available primary oocytes, only 400 of them gets a chance to form a mature oocyte. Only one of the mature oocyte out of the 400 will be released every month which can get fertilized when it comes in contact with the sperm. 
How does all this happen?
The hypothalamus produces a hormone called the gonadotropin-releasing hormone or GnRH. GnRH stimulates the anterior lobe of the pituitary to secrete follicle-stimulating hormone (FSH).FSH travels to the ovaries and stimulates a group of follicles to grow, were one of them will survive and become a mature follicle, the rest die.
FSH stimulates estrogen production. The increasing level of estrogen acts on the hypothalamus and the anterior pituitary to increase the level of GnRH and induce the production of another hormone, luteinizing hormone (LH). 
A surge in LH secretion triggers ovulation – the release of the egg from the follicle and the ovary.
Fertilization by a spermatozoon, when it occurs, usually takes place in the ampulla, the widest section of the Fallopian tube. The fertilized egg immediately begins the process of development while travelling toward the uterus.
Textbook of medical physiology, 11th edition , Arthur C. Guyton and John E. Hall.