I used to a lot but I've been slacking lately...I actually bought some of my uh. "fashion-challenged" villagers some new shirts but I've yet to send them out...
I used to send letters to all or most of the villagers every day in order to get rid of the crap I bought from Nook's/Able's for the sake of cataloguing. I got the gold letter badge pretty fast and there's not nearly as much showing up in either store that I haven't catalogued by now, so now I only send letters when I actually want that villager to wear a particular outfit or have a certain item in their house.
Actually, I've started sending cool-looking Nintendo items to villagers that I like so they'll have neat stuff in their houses instead of ugly shirts from the Able's.
But uh, as for actually writing things in the letters, I don't say much. "Hi. Here's an ugly shirt. Bye. STARSTARSTAR MUSICNOTE STAR."
Daily, including to my other characters. After i got the gold badge, i only send them whenever i have unused items. Mostly free item from tree and villager's gift.
Probably around weekly. I buy a few packages of stationery from my catalogue (I have my favourite ones in there) and send them presents out of whatever is bopping around extra in my wardrobe.