I think the best way to make an indepth character is to care about them and to care about continuity. One makes you interested in knowing the reasons behind their actions, learning what they fear or truly care about, in just knowing more about them in general, which is always helpful to round out your character. The other helps you build off the setting, the people who've affected them and helps ensure they fit the story. Both help keep you invested in the rp itself, too, which is always a bonus. ;)

Writing out their backstory without making it a slog to get through is a lot trickier... I have written 30 page histories that probably no one actually read in their entirety, and I have since decided that is far too much effort for everyone involved. It takes way too long. But a good rule of thumb is to know the key events that shaped your character into who they are today. You don't need to include all of them in your write-up, though if they might affect more than your character it's always a good idea to at least check with the GM before you cement them in. It's just good to have an outline that you can build on in the rp itself. 

Rule of thumb, if you don't want to get detail intensive, is to include family details (parents alive or dead, siblings? Important pets) and formative years (grew up poor or rich, tough love, no love, all of the wonderful memories or not). And then the event, or short series of events, that led to their current situation. 

Depending on how much you include, this can be two to three sentences or multiple paragraphs... But it should help cut down on extraneous info, if that's what you're trying for.