Start clipping NOW but keep in mind you won't start seeing significant savings for a few weeks. In other words, the huge extreme savings won't begin immediately, so be patient.
Clip only things you have either bought in the few weeks or currently have in your home. As time goes by, you can clip more coupons of things you want to stock up on.
Organize them. Some people organize by brand name, product type or date. You can use a coupon holder, binder of sheets w/clear pockets. I used baseball card sheets (9 pockets per sheet) but I also have a sheet of full size pockets I use for coupons that will expire in 1 week and another sheet of coupons that will expire in 2 weeks.
Use your coupons for only sale items. Never use your coupons towards anything full price if you can help it.
There are some amazing coupon sites out there...I like browsing couponcabin.com. But I only have a family of 3, no pets, and I don't like to stock up, so my grocery/household bill is probably $50/wk, which is very reasonable for me. I don't spend alot of time couponing but the time I do do it, I feel it pays off for my family just enough.
gl and have fun!