Once I know what my story is about, I do research on names for characters, story setting - if I've decided on a place for setting I research the area - if there is a sport/hobby that my characters are interested in and will be a key story element, I learn about it to the point where I can write with some ease on the subject matter as I layer it into the story. Whatever I don't know much about, I research if its pertinent to the story. As I write my first draft, I find myself noting where I need to research for the revision phase. Use Google, travel to the setting and stick around for a few days to gain its essence, learn about a hobby by doing it - but only know it as well as you need to to write the story, this will help over-writing details.

Biggest tip: don't conduct more than is absolutely necessary! Don't allow yourself to get bogged down in it. Research is great and useful and oft required, but it shouldn't distract you from the writing task at hand. Beyond that, we're so fortunate now with how much information is accessible at our fingertips -- online research often suffices. But I wouldn't discount perusing books or magazine articles on particular topics, watch documentaries, etc. Of course, if you can immerse in something yourself to garner first-hand knowledge of a place, a language, a culture, a sport, a field of study, etc., then more power to you. Interviewing (or merely chatting) with people already immersed in whatever it is you want to know about, that's the best!! Knowing how much is enough is a tricky bit, as we all know the required brevity in screenwriting. Simply not enough space to dazzle readers with everything you may have learned about a particular topic! Tempting, but ... not a good idea. You want subtle (and accurate) nuance, but you don't want to cram so much in you're beating readers over the head with it all. I think of proper research like basic condiments in cooking --- I wouldn't want to prepare a dish without having salt & pepper at my access. There may be a temptation to "pepper" a dish with semi-abandon to give it some impressive little kick, but too much can have your diners throwing utensils at you. However, just the right amount of "salt" -- the amount barely enough to know the dish has been salted and yet enough to bring out the flavors of everything else? Perfection!