for my job, the hiring process is notoriously slow & i know it'll screw my co-workers if they're without a replacement for a long time. i plan to give my supervisor, who's been a great ally in fighting for me at the job, an informal heads-up about 2-3 months before, like, "you know, i've been offered this paid graduate education and it seems likely i might take it.... i'll probably make a final decision & put in my notice in the summer... but maybe you want to start making plans for if that happens."
but then I'll wait to put in my notice with HR until 1 month before. I want my department to get the okay to hire, but i don't want to mess up my financial plans. we have a budget crisis every year around that time, so it's likely my job would get chopped early. in fact, i saw it happen to someone this summer.