First, you will need to determine the best size for you and where you will be using it. There are a few basic factors here...
a.) Overall size? - How strong are you and how long do you plan on carrying it around?
b.) Does it need to float? - Will you be searching in deeper water?
c.) What size holes? - How big are the things you expect to find?
I have built many sized screens ranging from 24 x 36 inches all the way down to my current ones that are 14 x 10.5 inches. To be honest, the big one has never seen any use (just too heavy to carry around). I will focus on the later as that is what I use the most often. Also, I have used the 1/2 inch and the 1.4 inch screen and found I prefer the 1/4 inch. You could also use a smaller screen if you are looking for smaller fossils.
Step 1: Materials
1 x 2 inch wood - you need a total of 46 inches per screen
1/4 inch mesh screen roll (sold back in fencing area in rolls) - 1 role will make many screens
1.5 - 2 inch wood decking screws (I use treated ones since your screen will be wet often) - You need 4 screws per screen so 1 box goes a long way
3/4 inch lathe screws (have a "built in washer") - you need 12 - 15 per screen
18 inches of cord for handles - I use parachute cord
The only tools required are a saw to cut the wood parts, a drill to make the hand holds, a phillips head screw driver, metal shears to cut the screen, and a tape measure.