Mostly repeats of other suggestions, but here's what helps me (though I still have clutter in places):
1) I actually have 2 dry erase wall calendars so I can see this month and the upcoming month. That way I also have fewer things that can't immediately go on the calendar. These can be pricey, but I got these at Walmart and only paid about $15 each, so if you look around you can find them without spending a ton of money.
2) Definitely try to deal with things right away - any forms get filled out and sent back to school the next day - that way you don't miss deadlines and can move the paper back out more quickly.
3) I also use the large magnetic clips - I have one for our preschool stuff and one with the elementary school stuff. That makes for easy reference for those papers (calendars, lunch menus, etc.) that I do hold onto. They will hold a lot, but it's not unlimited or they start to slide, so you'll also be forced to go through and purge if you haven't been good about keeping only what you need. I used to have these on my fridge, but decided I didn't like all that stuff on the fridge, so now it's on the side of a filing cabinet that's next to my desk. Find what works for you and use it.
4) I also have used a vertical file rack with a different colored folder for each child, plus one for me. That doesn't work for me now, but it used to be a good way to separate the "must-hold-on-tos" and keep them better organized.
5) For kids' school work (that they take such pride in), I have two ribbons/clotheslines in the kitchen with little clips so I can neatly display quite a bit of work. Periodically (when they're not around), I take down old things and throw away some and keep the special ones in our memory file and then fill in wth newer work.
I also second (or third?) the flylady recommendations - even if you don't use the whole system the mindset will help a lot. Just do what works for you and don't get overwhelmed with the rest.