I found this great green circular tablecloth in a Charity Shop. It's got a loose weave and is a linen polyester mix. The retro floral fabric is two pillow cases that I found a couple of days later in another Charity Shop. Got a green thing going on, apparently...
When using thrifted fabric you can't always tell what the fibre content is. I like to know what I'm using as I prefer natural fabrics. I found a great way to find out what your fabric is made from, it's called the burn test.
You take a small square of fabric and set fire to it (safely! in suitable container - not how I do it!) If there's a smell of burning paper then it's most likely cotton. If there's a chemical smell then there's some synthetics present.
Once the fabric piece is all burnt, poke about in the ashes. If the fabric is cotton then the ashes will be soft and turn powdery when you touch them, if there are any hard lumps, that will be melted synthetic.
There is a little more to the burn test, but I've found that these two main points are the most helpful and all I need to get an idea of the fabric I'm using.