OK. Ill try to show you how I do it. Not every time, and it is just a basic scheme... but anyway:
First take some trait, or idea, or that you find interesting. And take it to grotesque. Like "This race always keep promises", "This race care for Mother Nature above all", "This race never surrender". In the game I currently play it is like " this race is primarily motivated by the fear of death"
This would be their main theme.
Explore this theme. Think of how this race came to be embodiment of this theme. Think of what will suit it in Stellaris game. Look at the lists of trites/ethics/civics.
-For my current game I find, that it would be interesting, if my terrified of death race should by extremely long lived - they spent so much of it`s efforts and resources on living longer! Then I think that they mast be Fanatic Spiritualists - religion traditionally gave them at least some safe harbour from fear. And, in the same time - I just understand, that their ideal ascension is totally different - it is synthetic evolution, becoming immortal robots!
Yep, I really play THIS. It is super fan)
Then try to think of it in a more concrete, detailed way. Try to think of what looks like a logical conclusion from the concept you already have. In my case it was something like: OK, so they are afraid of death, that means they behave quite cowardly in buttles. So, they need some slave/robot solders to fight for tham!.. But do they have slaves?.. Well, they are longlived, and for a longlived race it seems reasonable not to treat some other "fleeting" like equals... OK, so they are slavers! But they are not brave enough to just go and attack somebody equal... So, they would attack and enslave primitives, or somebody already losing a war! OK, so they are cowardly sneaky slaving bastards! Do I what to play them like this? HELL YEAR!"
Then try to understand, that all of this will mean I the game, what you will actually do.
In my current playthrough I have several principles:
-Act like a coward and traitor. Stab in the back, avoid straight conflicts
-Enslave primitives - by Covert Infiltration, if possible, cause it is the most "safe" way
-Take every possible tech or anything else, which will give us at leat several more years of lifespan
-Find a logical explanation of changing Ethos from Fanatic Spiritualist to Materialist
-Finally achieve the goal of becoming immortals by going full synth
Then, after you begin the game, try to accordingly to this principles. Not mindlessly or suicidely (if it`s not one of princilpales!) - remember, your race also want to win! Remember, that your Empire is not a statue to it`s ideology, but a changing society. If you see, that It is logicaly moving some other way, then you initially imagene - consider letting it go there it goes. In one of my Try to see your leaders not as a modifiers, but as a real leaders, heroes and villains of your story. I said that my curre race is a slaving one, but if i Suddenly see that my God-Emperor leads the Egalitarian fraction, I would seriously consider at least give slaves better life conditions)
OK, this is how I do it in general.... but again, sometimes I just tell myself "What if tolkien`s enth became mad and try to destroy all the saintient creatures, because they are harming NAture!@Cheers, and hope it was usefull!