It depand on the game . In DAO for exemple , the beginning set the tones . Then , some more research about for exemple the city elf origins . And that made me find peoples who gave me a good reason to play a city elf that wasn't all human hater and full of wanna kill everyone (which is what I was doing everytime) . I find some games more restrictive then others .
In DA2 , I had an easier time making up my 3 Hawkes . Hawke tone (sarcastic , noble , jerk) helped me flesh out a good reasons for their actions..and what morale compass they had .
The game I had the most fun tweaking stories for , was probably Mass effect with the 3 background and the 3 reps . I looked those as well , and had alot of fun seeing peoples mix and match and give their reasons as to why .
I have around 20 f!shep with differents stories , similar romance but different reasons an morale compass . 
There are games , where my imagination fail me though . Skyrim is a good exemple . Even though I had a good background for some of my charachter...the game being soo big , the dialogue being limited in tone....they really didn't make it far and died often . (as in delete) . So yeah , I generaly go from what the game give me..and work with it and around it and come up with something . Although this forum has been a hive for inspiration..I have so many females Inquisitor ..cant wait to try them all out