Have a bin in your kitchen to collect daily compostable items. Keep it somewhere in your kitchen that is super convenient and will be a reminder to you and your family to compost as much as you can!! There are all sorts of little "kitchen compost bins" you can buy that are aesthetic and would blend right in with the kitchen....everything from plastic pails to nice stainless steel pails. If you have the extra cash for a nice pail that is great, but if not then you can always use something homemade :)
Put whatever compostable kitchen scraps you have throughout the day and then at the end of the day (or every other day...just dont let it start smelling) take it out to the compost pile or compost tumbler and cover it with some "green matter".
Sometimes I carry my kitchen compost bin outside to dump it right into the compost pile and sometimes if I have alot (when my bin is full and I cut up alot of veggies and have scraps) then I put it all in a large compostable brown paper sack and just put the entire bag in the compost. (Tip: next time you go to the grocery store and forget your grocery bags...ask for paper, not plastic!)
This is a good list of "What to Compost"... most lists Ive found are CRAZY long and just about get overwhelming before you even start composting! But this list (in the link of "What to Compost") is a good brief yet explantory list of what you should and shouldnt compost. You can do more research (and if you are planning on composting I do encourage alot of research) just search around on google :)