How were babies delivered during the time of Abraham, Isaac, Jacob and Moses in The Holy Bible?

Most women gave birth with the help of a midwife. They cut the umbilical cord and took care of the baby immediately after birth. There were no hospitals. Many women died in childbirth and many babies died soon after birth. People have been having babies for thousands of years before modern medicine was available but modern medicine greatly increased the chances of survival for both mother and baby. 

You don't have to go back to biblical times to find societies that don't have hospitals or physicians. It's still happening today all over the world.

Women give birth the same way animals do--by themselves without hospitals. There's often a midwife or tribal elder who can assist if necessary.

There were no physicians or hospitals, babies were born at home attended by women who had training or experience with babies.

Midwives.................

Hospital delivery is a mid-20th century thing. Babies were born at home with the help of midwives for the vast majority of history.

Same as they are now, by a stork obviously. Hey, if God exists then that myth exists as well.

There were women called midwives that had experience in helping other women in giving childbirth - Exodus 1:15 - Later the king of Egypt spoke to the Hebrew midwives whose names were Shiphrah and Puah, - - - -
Exodus 1:20 & 21 - 20 So God dealt well with the midwives, and the people kept increasing and becoming very mighty. 21 And because the midwives had feared the true God, he later gave them families. - - - - It is good that you ask such questions to further your Scriptural knowledge. Please note that God wants you to have an accurate knowledge of the truth - 1 Timothy 2:4 – whose (God’s) will is that all sorts of people should be saved and come to an accurate knowledge of truth. - - - - And that Scripture also shows that taking in accurate knowledge leads to salvation. Like Jesus' words here - John 17:3 - This means everlasting life, their coming to know you, the only true God, and the one whom you sent, Jesus Christ. - - - - However, the Bible does warn us about some that will twist the Scriptures - 2 Peter 3:16. . . and these things the ignorant and unstable are twisting, as they do also the rest of the Scriptures, to their own destruction. - - - - So, we have this Scriptural advice from God's word to protect us from being misled by those that would twist the Scriptures - Acts 17:11 . . . carefully examining the Scriptures daily to see whether these things were so. - - - - So we should always examine the Scriptures carefully to make sure we are getting accurate knowledge that leads to salvation. And Jesus' words tell us clearly that God's word, the Holy Scriptures, are the truth - John 17:17 - Sanctify them by means of the truth; your word is truth. - - - - There is no greater treasure to be found. Bible truth liberates us from superstition, confusion, and morbid fear. It gives us hope, purpose, and joy. Jesus said: “You will know the truth, and the truth will set you free.”​—John 8:32. - - - - Yes, Jesus assures us that we can KNOW the truth. And that truth from God's word will set us free from being misled by those that would twist the Scriptures. With that in mind, I invite you to visit the following web site where free Bible lessons are offered online. But ALWAYS examine the Scriptures carefully to make sure you are getting accurate knowledge. The site is:
www.jw.org

It's a natural process.  Also, there was a ~5% chance of death in childbirth.

Babies were born at home, with other women helping the delivery process. The use of mid-wives were common practice. You must understand that childbirth is a 100% natural process.

There were midwives. Shiphrah was one of the Hebrew midwives who, together with Puah, was commanded by Pharaoh to kill all the Hebrew male babies immediately at birth. Being a God-fearing woman, however, and having respect for the sanctity of human life (Ge 9:6), she preserved the boy babies alive and was blessed by Jehovah with a family of her own.—Ex 1:15-21;

What are you trying to use as a point?. Life expectancy was still short, people back then believed evil spirits caused ailments? And medical operations were still faulty. Modern medical science is still way better the anything they wouldve had.

i think DHL was around then