It depends, some Satanists believe in Satan as real and try to emulate his positive qualities.
But many do not and see him as a literary figure by which to see as a metaphorical narrative. There is a lot of disagreement on that. Some groups are hedonistic while some take from works of literature where he isn't as hedonistic but is more about enlightening people and fighting injustice.
Again, it really depends on who you ask. There are many Satanist groups and most disagree with each other a lot. In the end it always comes down to what Satan means to the person.
With all of that said I *can* answer for me, both as someone who has been involved with Satanism for several years now. When I was younger I thought Satan was an actual literal being that was separate for me. My understanding was kind of limited but over time I began to realize that Satan isn't one thing but something that someone is and becomes.
This is where it becomes hard for me to fully discuss this in language that doesn't borrow from Hinduism... but there is a concept in some sects that is essentially a 'personal god' or deity by which one is inspired. For me, Satan is one that inspires. When I think of being Satanic I think of Rajoguna (energy, passion, ego-driven, changing, motion) and a strong, undeniable urge to speak truth and discover it, and 'bear light' so to speak to reveal these truths to other people. The truth doesn't have to be religious, but it has to be something that helps people. I find myself striving to be a warrior of sorts to fight injustice and lies and deceit. I hate to see people treated unfairly and I hate to see people manipulate others and lie to them.
I find Satan to be a good narrative, a good figure by which to explain my personal preferences and ethics, by which to paint my spirituality in tone and in symbols. Satan has meant a lot of different things to different people, and perhaps I am influenced more by some groups than others. Sometimes I wish I could find different symbols seeing as how misunderstood Satanism is in general, but I've had too many experiences with "Satan" and I am too drawn to it and philosophically much of Satanism speaks to me. I think for a lot of Satanists it's the same way... there is a saying that "Satanists are not made, they are born." For a lot of us, we are Satanists because we cannot be anything else. It's simply inside of us and we can't escape it; like a planet in orbit, it isn't something you would want to escape, because it's simply where you're *supposed* to be in the first place. It's simply the reality of our existence.
To get more specific with your question sometimes I use invocations and chants, in a way someone might do with other deities to praise or worship. But for me it's about the meditational place I go to and focusing on making myself more aware of who I want to become. To me, being Satanic is being my best self and overcoming hardships and those who oppose me and what I stand for. It's about transcending all the nonsense of this world and our weird, arbitrary society to accomplish something meaningful and fulfilling to me personally, which most often entails either furthering my musical talents and work, or doing something that will help other people.
I guess another simple way to put is that I show devotion by living by my values, I just hope my longer explanation showed how that relates to belief and symbolism, and maybe some of what that entails.