-Keep up with what you need through either moridb, or a spreadsheet
-go to all the shops daily and buy what is missing, marking off items. If you don't have many, it's best to buy them all just in case
-take advantage of streetpass homes. You can order 5 items per day for each character, so if you have 4 characters, you can potentially get 20 new items per day
-dig up everything you can and try to collect all the gyroids/fossils. You can keep track of these on moridb as well. There's a thread somewhere in retail where someone will let you catalog all the gyroids for free, I recommend it
-buy genuine art every time Redd comes to town to complete your art collection
-buy all the stationery you can
-participate in bug offs/fishing tourneys to get trophies
the best thing you can do is just buy as much as you can everyday, be diligent, and keep a list.