Now that your stock is cooled you are ready to strain it. There are several ways to go about straining stock. If you want or need an extremely clear stock I suggest using a chinois. A chinois is a very fine sieve and will keep any bits out of your final product. I have only done that when I worked in a restaurant, at home I don’t care if there are some tiny particles in my stock.
Go grab your colander that you use for straining pasta and get a big bowl with a wide mouth. If you lack that you can use a smaller mouth bowl but your colander will also have to be smaller. Set your big bowl in the sink and put your colander in it. My counters are too high for me to pour the stock out, so my bowl goes in the sink. No one ones several quarts of stock everywhere because you lost control of the pot.
Now that you have done that you can start pouring I do about two quarts at a time. Get what you are going to store or freeze your stock in. I like ziplock bags. Take a measuring cup, scoop, and than pour into the bag. Decide how much stock you want in each bag. I do quarts and than some two cup bags. I lie the bags flat to freeze they stack well.