Once deposited within the vagina, the sperm swim through the cervix and into the uterus, and then up into the fallopian tubes.

Fertilisation occurs in the fallopian tube

Only one sperm will succeed in fertilising the ovum, by penetrating its cell membrane and depositing the male genetic material into the female cell, where the two nuclei fuse (as in the picture below). 

After fertilisation, the fertilised ovum (zygote) remains in the fallopian tube for about 72 hours, and during this time it develops quickly.