We ask through our website, in the parent communication area and sometimes on our Facebook page. Especially Facebook if its a last minute need. When we welcome new parents we explain this needs list and that just because it is on the list does not mean they have to provide it and it does not mean that it has to be brand new. We encourage parents to bring what they have from home that they are no longer using. We don't need parents to run out and buy yarn for us if they have some at home they don't need anymore. We also let parents know if they are cleaning out their homes to bring in anything they do not want, if we can't use it we place it in FREE bin by our front door and share with all the other parents. When the box contents sit there for a few weeks and no one is taking anything then we make a run to Goodwill and donate it.
We have parents bring items in and we stock them in our supply/craft storage, we may use them immediately or somethings may wait for longer. I don't know how many times myself or one of the other teachers have been found just staring at the stock of stuff, trying in their minds to create something out of a supply that has been around for awhile. For example, a parent brought in heart shaped wood chips, they were cute but we had no idea what we were going to do with them! They ended up being our Bingo chips! We wrote the ABC's on them and put them in a drawstring canvas bag someone else brought in and now when I call Bingo letters I pull the wood chip letter from the bag!
We have always found a way to use whatever is brought in and for some parents its really fun for them to see what we create from the items they bring in.
My suggestion is that you start a needs list right away. The needs list is not mandatory and parents shouldn't be made to feel they HAVE to bring these items in, but I think you will find that if you don't ask for the items to be brand new, parents will willingly bring them in.
Some needs, like food items, we need on a specific date, for this we use sign up lists. The lists hang in the parent communication area and we put it up weeks in advance, with the specific items we need and the date we need it on. We do food this way so that we know the items is coming in and who is bringing it. Placing it out a few weeks in advance also gives parents time to budget buying this extra item when they go to the grocery store.
For all other items we just have a list and when enough has been brought it we scratch the item out.
Give a needs list a try, you might be surprised how willing your parents are to help out, these are their children, they care about them and if bringing in paper plates is a way for them to help out they most likely will do it!