How can I reference other artists’ work in a way that's still my own?

The key to this would be to deeply consider all the aspects of that artist's work and then find what speaks most to you. This would mean looking into the artist's cultural background, the historical and political context of the time they were alive, if they were a part of any art movement, the mediums they use, the scale they traditionally work at and the colour palette they most commonly use. It's also important to see if they have consistent subject areas they like to address. All of this is important so you can fully understand how and why the artist creates the work they do and then put your own spin on the aspects of it that you like.
For example, I love Frida Kahlo's work and I wanted to reference it in my work. At first I was drawn to her use of surrealism, and then I found out that her work has a lot of cultural and personal significance to her. For example, she directly shows people and events of her life as well as important symbols of her cultural upbringing in her work, and uses surrealism not to portray dreams or fiction, but to express her feelings towards these real events in her life and these parts of her culture. So for me this was an aspect I really liked and wanted to reference in my work. To do this, I decided to experiment using surrealism in my work to portray my own experiences and culture in a more emotional and personal way.