Archangels do tend to be rather specific in the areas they aid humans in. Perhaps the situation or events in your life during their arrival can give an idea as to why they appeared. Finding out more about the angel could help figure that out. If you feel they have been reaching out to you, and you want to work with them, then reaching back and establishing a relationship with them would be a good next step.
As to how to do that: There are a few different ways to communicate and work with the archangels. The archangels have individual topics and subjects they are corresponded with. People typically start out forming a relationship with prayer, since most find that the archangels tend to be rather accessible and open to helping humans when petitioned for help in their area of expertise (though not always, and it also depends on the archangel. Cassiel, for example, is known as an angel said to keep distance from humans and help from afar).
Many people also will use candles, oils, incense, cardinal directions, crystals/gemstones, and flowers that correspond to individual archangels as gifts, offerings, and rituals. For example, Gabriel is traditionally associated with white flowers as well as lapis lazuli. Astrologically, the moon is under angelic rulership of Gabriel. So anything moon-related would work well when establishing a connection. You can create an altar for the archangels you want to work with. Make it a center for communication and establishing that connection. Set up your space, begin the prayer or ritual. Then listen out for messages and answers. Use your psychic senses - sense the presence when the angel has come forward (funnily, Gabriel is called on to hone psychic senses such as clairvoyance).
Different archangels tend to have different feels to their energy that make it easy to identify them when they come, with practice. I like Michael, he's nice, though as Bianca noted, he tends to come across as rather flat, emotionally. And that's a common experience and identifying feature of him. Make note of what communication you receive. Then, it's in good form to thank the archangel for hearing you out before closing things up.
There are different rituals you can use to invoke the archangels. Most of them will be specifically for Michael, Raphael, Gabriel, and Uriel. I highly recommend the Communicating With the Archangels book series by Richard Webster. He has a book on each of some of the most popular archangels.
They contain the canonical history of the archangels in question across various cultures and religions, ideas for rituals (both traditional and more modern) and communication, correspondences, etc. I like how compact but thorough he is in outlining the different aspects of these spirits across Christianity, Islam, Judaism, and relations and influence to Babylonian and Egyptian culture. They're really good reads if you want to focus on a specific archangel and how best to relate to them.
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