How to develop a character from a script

How do you develop a character from a script?
There is a very simple answer to this: READ IT...
(...and understand it a little too.)
All of the best actors have said it, in interviews found all over the web- to effectively play a character, they always go 'back to the text.' So what does that mean? Well, at the end of the day, a script is essentially a more specific way of telling a story- it combines both the narrative and the way to convey this narrative at once. It isn't scientifically laid out in diagrams, nor is it as informative as an instruction manual per se, but they're there- those key elements telling you what you have to do. A director will have brushed upon them, but they're really looking at the bigger picture (pardon the pun.) It's your job to become part of the bigger picture, and help convey that story- a story that is back in the text.
So read it, again and again. Not just your bits, either, read everyone's lines and directions. More often than not, the character is established in an audiences minds before they even enter- as other characters and directions will create an off-stage presence that you will then fill. After all, in reality- if you're describing someone, you're not usually doing it to said person, you describe a person to others (to put into their heads an idea of who they are.) So in the basis of a text, usually you can find descriptions of who you are in scenes that do not involve your character, to put into an audiences head who you are. So read them, study them and make sure you're fulfilling what the writer is having the other characters say.
Obviously read your own lines and actions, and read into your own lines and actions. If you say you will do something, and then your actions say you do the opposite, then your character is a liar. If you're described as having different lipstick shades on your collar then you are possibly a womaniser if you are male, and clumsy if you are a female. Little hints as to who you are probably exist in the obvious forms of text- sometimes the writer will just out and out say you have these characteristics or those characteristics- follow them, perform them- they are obvious for a reason.
However, how do we develop a character?
Well, that's perhaps not so obvious- sometimes, the script has given you all the lines, and all the actions but the writer has left it to your interpretation. So, what do you do? Well, have you ever heard the phrase 'reading between the lines.' Voila! This is where it makes the most sense! Scripts have several components to help them blend action and story together- Context, subtext and character are a few. You can really use the first two to help create the third. So, let's get hypothetical for a moment. The scene is as follows. You're in an office, and a co worker walks in and offers you a contract, which your character has got to sign. But you shake your head and tear it up before walking out. The other characters on stage gasp at this as the lights fade. Ok, it's a hammy example but it's simple. No lines, just actions and plenty to play with. The context in this case is that the scene is an office setting, so your character works in an office, it would appear. So, you're probably smart then, well groomed- after all you do work here. Also, is your character hot tempered? I mean, s/he did just tear up a contract and leave... They seem to be of few words... They don't like paper? All of these ideas are from reading one scene- not a lot to go on just yet. But if you were made aware by the writer/ director/ text that the co-worker is an old flame with whom a relationship went sour, or your character built the company and it's going bust, or even you have just been told you have months to live- all of these count as subtext, by the way- then how you play the scene becomes much more obvious. The subtext alters the scene, because it alters how your character would approach things, and how your character would approach things with all this information is now up to you.
So think big, read it all. Then maybe read the beginning, then the end, then the beginning again, and see what your character gets up to. Provided it's a linear narrative, there should be a clear idea running through of the journey your character goes through. How do the things that happen affect your character, how do the things from before the script start affect your character, what happens next? Then think, how would they affect you as a real person, not a character? Because half of the characterisation is getting cast, remember- you already embody the basic characteristics to make your role work, all that remains now is to develop it. So bring it home, ask yourself what would you do, how would you do it, and why? Then read it again. Then again.
By now you've gone 'back to the text' and it all makes sense...