I'm a Time-Whore(TM). I used to use a historiography book to calculate what the calender dates were for my campaign. Now that computers are used at game, I just open up the calendar, forward to 2070s, and see what's what.
Every run I make I note the start date (usually when the characters meet the Johnson). From there, I just keep quick running notes;
10:05 PM: Meet Johnson.
11:32 PM reach warehouse
NEXT DAYS DATE
1:31 AM Firefight at docks
1:32 AM Firefight ends.
etc.
For downtime the official GM line is; "everyone tell me what you're doing, we'll figure out when it gets done in a perfect world, and the caveat is I may interrupt anytime with something outside your plans." When I do interrupt it doesn't take long to push back the character's plans accordingly. "You were supposed to roll to learn that new skill on the 16th, but because of that whole little Yakuza issue on the 12th and the resulting hospital stay that day, your roll now counts for the 17th."
With characters using contacts to buy restricted gear (which takes time), learn skills (extended tests, 1 week), program their own software, found magical groups, etc., I find it's important to keep track of time accurately so it adds "life" to the campaign.
One example from last game; a pc had been flirting and courting a beat cop contact of his and while getting some info from her on the previous session he offered to take her out on a date...next Friday. Great. The player starts keeping track of that while we're doing downtime last session, and keeps asking me "what day of the week is it," and I'm telling him. Then Friday comes around and they go on their date and then he says, "Wait? It's Friday, right. The 14th. Of Feb (2070). I'm taking her on a date on Valentines!?"
It's the little things that make the extra date-keeping worth it, at least for me
I also made a detailed timeline from Emergence and Runner Havens (Seattle section), recording the date for every upload/news item/etc for 2070. So I can then introduce relevant bits and pieces along the way. I throw out info now and again, especially during downtime, so in-character the player's get to see bits and pieces of the main SR storyline(s). Like the character on his date, asking if she new places in Seattle to lay low, she's just a beat cop, not real sure, mentions "the barrens if you're brave," and then launches into a dinner long complaint/worry about her job, and the flack all the departments are taking for not finding the Mayan Cutter, and that when her Lieutenant isn't breathing down her neck she's watching some news anchor that's lambasting Lone Star for their ineptitude.
For me, my favorite thing about Shadowrun is the "story," the woven history to create a different world. So my players have to deal with me trying to translate my love for what I've read into game in an effort to immerse as a part of that (living) history. Of course all that takes a back seat during runs, so downtime is where I (mostly) get to introduce it.
Anyway, that's the overall gist of how I do it; complicated and involved. But the key is to have fun, everyone to have fun, so every group will be a bit different.
