The desire to call upon angels for help and guidance is an ancient phenomena, and while many people today casually ask for divine help through prayer, there also exists a very complex system for obtaining assistance from Heavenly creatures.
This complex system is tied to the ancient Jewish magical system of the Kabbalah, an esoteric religious philosophy intended to explain the relationship between God and the Universe (with humans somewhere in the middle). In theory, by studying and employing the Kabbalistic system, one could uncover the divine secrets of the universe and gain power over the workings of the world (such as the power to part the Red Sea).
Kabbalistic scholars examined the Book of Exodus (Chapter 14, verses 19-21) and determined that it contains a very special and magical 72-letter name of God. This name is considered unpronounceable by human tongues, but more importantly, it can be broken down into three-letter words that are actually the names of 72 angels.
Then the angel of God who was going before the host of Israel moved and went behind them, and the pillar of cloud moved from before them and stood behind them, coming between the host of Egypt and the host of Israel. And there was the cloud and the darkness. And it lit up the night without one coming near the other all night. Then Moses stretched out his hand over the sea, and the Lord drove the sea back by a strong east wind all night and made the sea dry land, and the waters were divided.
The 72-letter name of God is called the "Shem HaMephorash," and therefore, the angels whose names are found in the passage of Exodus are called the "72 Angels of the Shemhamphorash." Each angel has a specific duty and a belongs to a specific choir of angels. These 72 angels also rule over 72 demons, the names of which can be found in many magic books dating from the second century onward.
Although the magical system for evoking the 72 angels has existed in a codified form for over a thousand years, it has been highly corrupted from the original Hebrew in which it was first written. Many of the later texts have either never been translated into English, or were incompletely (or incorrectly) translated. However, there are a large collection of magic manuscripts dealing with angel evocation in the French language, which can still be studied today.
The basic components for evoking an angel is the angel's seal as well as the spoken invocation. With these together, one should be able to make the angel appear before you and do your bidding. However, in the grimoires from the 1700s, the first texts that actually attempted to draw out the seals and sigils of the angels, there is significant variation between texts, to the point that three completely different sets of seals have been created for the same 72 angels.
These differences make the process of actually evoking the angels quite challenging, especially since most of the existing sigils don't utilize the strict method for drawing the circle and name of the angel. All these challenges can only be overcome by diving deep into the ancient manuscripts and trying to trace the seals and information about making the sigils back to its earliest point. However, it would appear that some of the ancient texts have been lost and may never be positively identified.