Some diseases can be transmitted to babies during delivery, like herpes, gonorrhea, syphilis and chlamydia. Syphilis can even cross the placenta and affect the fetus. HPV is not typically a problem, thankfully.
During pregnancy, if you had a positive HPV test in the past, it's not unusual for HPV on a Pap test to be positive again, even if it has been negative for a while. Pregnancy is a time when your immune system is down, and the HPV can pop out of dormancy temporarily. Usually, after birth, it goes away again.
HPV does not cross the placenta, so it doesn't affect a fetus. Even if you are positive for HPV during pregnancy, your developing fetus is fine.
Now, some women who have genital warts caused by another strain of HPV can pass HPV on to their infants during vaginal delivery. The infants then have warts in their throat or on their vocal cords. Even then, they don't usually have to be treated.
The HPV strains that cause cancer are not passed on during delivery. You won't have to have a c-section for that reason. You can have a regular vaginal delivery and not worry about passing on HPV.