Those big spools of thread usually have a cone shaped center, there are adapters you can buy that fit the inside of them - you just place the adapter on your regular spindle.
My old Brother's spindle broke off and can't be replaced so I use a empty jam jar to hold regular spools of thread, just place the jar behind my machine. It's kind of annoying because it does make a lot of noise so I'm looking to buy an spool holder but not the plastic ones Joann's had.