How would you figure out how much fabric is needed to make a knee length dress?

The pattern should give a clear indication, because it will generally include the cutting requirements for the fabric (assuming it’s not a patterned fabric that will require special cuts to carry a patterned figure from one cut piece to another, anyway), and depending upon the height and size of the wearer, which should be indicated there, too (or show adjustments / allowances / corrections to be made).

But I wouldn’t know for certain, not having seen a paper pattern for the last 50 years or so, from when Mom used to make some of our clothes.

Go to Joann’s (or equivalent in your area) and find a pattern that comes close to what you want. All the instructions are included. Patterns aren’t expensive.
Good luck with this!

I agree, find a similar pattern to what you want and check how much fabric it calls for.

If it’s a dress made from just two pieces of fabric it should be easy to estimate, but if it has many panels or accessories made from the fabric, then it can be more tricky to lay out the pieces the optimum way to spend the least amount necessary on the fabric.

The pattern should tell you how much fabric you need as well as a suggested way to lay out the pieces so they are cut out the right way. Some pieces, for example, might need to be cut on the bias of the fabric, while most others will need to be cut so that the ‘arrow lines’ on the pattern runs along the grain of the fabric. I can help you, if you can digitise the pattern or refer me to a website that might feature it. How many pieces in the pattern?

Here is a good website resource. http://www.blueprintsforsewing.com/blog/archives-2

Linen dyes well. Could you find a 100% linen dress ready-made?

It depends on the pattern, as others have said—and the size! You need more for a size 14 than for a 2.

I had a friend who said she could make anything with 2¾ yards of fabric; but she was an expert. (She was also very heavy.)

Little details make a difference. If you go sleeveless, it will require about half a yard less than if you opt for sleeves.
A full skirt (loose, flaired) will require a full yard more than a straight skirt.
@canidmajor is correct that use of a pattern would be best. With a pattern, full instructions for layout and assembly are included. That is important, because things like the grain of fabiric must be right. If not, then after washing, you could have a dress which twists up like a barber pole.
Making your own pattern should not be done until you are practiced enogh to look at clothes on a rack an know exactly what the yardage and layout was for them.

There are a couple of quick cheat ways to figure it out but… it’s best to have your pattern first. There are a lot of good free patterns online. Look them up – pick a simple one that has a shape you like – apply your measurements – it will tell you how much fabric you need..

I often buy plain white sheets for projects like this – you can get 100% cotton fairly inexpensively.

This is a super-simple alternative. Buy a long white cotton skirt at a thrift store and repurpose it into a shift dress.