Conception is when a sperm cell and an egg join together. For conception to occur, a sperm needs to come into contact with an egg and fertilize it. It happens (most often) during intercourse where the penis enters the vagina.
Pregnancy can be confirmed when the embryo settles in the endometrium (thin lining inside the uterus) - usually 2-3 weeks after intercourse, when a certain hormone (called hCG) can be measured with a pregnancy test. When counting the days of pregnancy, however, counting starts from the day the last period started.
Pregnancies are measured in weeks and days and start from the first day of the last period - but that day takes place before the conception itself!
There are methods of conception performed by doctors, but it is most often used by those who have difficulty with conventional conception or who are not in a heterosexual relationship.