Step1
Find you a good work area and a place to dispose of old deck material.
Step2
Use your Circular saw to cut across the deck planks. You may need a hand saw finish cutting through the edge planks.
*Remember to remove all the wiring before cutting. This can be reused.
Step3
Measure the length of one of these planks and that is the size lumber you will need. Example: On a 12' trailer they would most likely use a 2x8 12 foot long.
Take out the old wood and dispose of it.
Step4
Most utility trailers are made of angle iron and typically the deck planks are put in and then an end cap is welded on to hold them in.
Cut your lumber to length. A good tip here to make this easier for install would after you cut to length on one end or both cut of the four corners of each end of your deck plank. Just a small piece of the corner this will make it easier to install.
Step5
Now that you have the decking out and the new planks ready to go in, let's put them in.
Put the planks in at an angle drop in and slide into place. If you did not cut the corners off you may need to use a sledge hammer to get them into place, once the are in place they are usually (not always) easy to push to the edge of the trailers
Move decking to either side of the trailer alternating sides until you can not fit any more decking in.
This should leave you with 2-3 gaps where you could not twist the lumber into place.
Step6
For these last 2-3 pieces you will use another method to get them in place.
Place one end into the top channel
Place a floor jack in the middle of the trailer (on the ground of course)
Using the floor jack as a fulcrum, bend the board over the jack into the rear channel. (You will need to hold that end in place while you have a helper release the floor jack and the board will straighten out and pop into place. Do this with the remaining boards.
**** TIP -- You may want to soak these boards in water before doing this as it makes them bend easier. ****
Step7
When you have all the decking in there will most likely be small gaps on each side of the deck you can cut small spacer blocks and hammer in the gaps between the lumber and the frame of the trailer
Step8
Use self tapping screws and screw the deck down to the angle iron frame.
Step9
Re-run your lighting wire and make sure your lights work and your done.
Re-Deck your Utility Trailer
Use your Circular saw to cut across the deck planks. You may need a hand saw finish cutting through the edge planks. 
Measure the length of one of these planks and that is the size lumber you will need. Example: On a 12' trailer they would most likely use a 2x8 12 foot long. 
Most utility trailers are made of angle iron and typically the deck planks are put in and then an end cap is welded on to hold them in. 
Use self tapping screws and screw the deck down to the angle iron frame.
Re-run your lighting wire and make sure your lights work and your done.
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