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.
Step 2: Cutting and Assembly
Next I attach the screen to the frame with the Lathe Screws. I place the screws about 3 - 4 inches apart all around the frame ( no need to be exact here). It normally takes 12 or so screws to complete.
Lastly, I drill two holes on each of the short sides of the frame. I drill these about 4 inches apart but comfort is the deciding factor here. Once the holes are drilled, I feed in a nine inch length of the parachute cord and knot the end. I then feed the other end through and knot that as well. Repeat the exact same thing on the opposite side. These form the handles.
Step 3: Fossil Screen Use and Options
Some optional "enhancements" to your screen include:
1. Adding a ruler along the top on one side of the frame. This will help when you take pictures of your finds to get an accurate size.
2. You can zip-tie on lengths of foam (from pool "noodles") to help your screen float in the water next to you. (If you add the floats then you will also need to add either a long leash that you can connect to yourself or some type of anchor system to keep it from floating off downstream).