Abraham commissions Eliezer from Damascus to find a wife for his son Isaac and confirms this commission with an oath.  This ancient custom of confirming a solemn oath is described in the Targum of Jonathan ben Uzziel, called the Jerusalem Targum.

The ceremony used on this occasion of the servant putting his hand under the thigh of the person to whom he was to be bound means that he put his hand on the part that bore the mark of circumcision, the sign of God’s covenant.  While this may seem vulgar or profane to us today, it was the sign of the covenant between God and man and confirming a covenant in this way was actually a sentiment of reverence and godly respect.  We must understand that there is a drastic difference between our cultural understanding today and their culture at that time.

 Abraham sent his servant quite a distance to find a wife for Isaac. Nahor was about 600 miles north from where Abraham was living. It was between the Euphrates and Tigris Rivers near the present day Turkey border.  No doubt when Eliezer made this journey he passed near his ancestral home in Damascus.

Abraham's servant prayed a very specific prayer for requirements of choosing a wife for Isaac. He prayed that the future wife for Isaac would not only offer him a drink of water but would offer to water his camels as well. The hospitality of the day required that women at the well offered water to travelers, but it was not the custom to offer to water the animals. When Rebekah offered to water the ten camels, she understood how many camels there were and how much water that would be for that many thirsty camels.  And she didn't offer to just give each camel a sip.  She offered to water the camels until they had finished drinking.  Estimates are that it would take about 25 gallons of water per camel after a week's journey. Wonder how many trips she made back down into that well.  Later on in the reading we are told that Rebekah had several servant girls attending her...so why was she going to the well instead of the servant girls?  Just another example of God's providence?

This well was probably not the "Jack went up the hill" kind of well with a bucket on a rope to haul up water.   Most likely there was a subterranean pool or spring and a cavern was dug down to the spring with manmade steps leading down to the water.

Notice when the servant prayed, his prayer was answered even before he had finished praying. Similar to what happens to the prophet Daniel

Daniel 9:23

As soon as you began to pray, an answer was given, which I have come to tell you, for you are highly esteemed. Therefore, consider the message and understand the vision:

Can we be sure that as soon as we begin to pray that God will hear and answer our prayers? Are there some things that may hinder our prayers?
James 4:3
When you ask, you do not receive, because you ask with wrong motives, that you may spend what you get on your pleasures.

Abraham's servant's motives were pure. It was an unselfish prayer on his part. He didn't ask for success for himself, only that God would show kindness to his master.

How is it with us believers? Do we pray with the wrong motives or attitude or do we pray in faith that God will answer our prayers in His way and in His time?
Psalm 5:3
In the morning, O LORD, you hear my voice; in the morning I lay my requests before you and wait in expectation.

Do we lay our requests before Him and wait in expectation for the perfect answer? Wouldn't that be a great way to start every day?