Since you intend to tie the arbor knot for fishing, so the fishing line will be used instead of a piece of rope. Thread the fishing line in a number of loops around the to-be-tied object. As far as fishing goes, this object may be a fishing reel or you may be tying the knot for a fly that you intend to try.
Now an overhead knot needs to be tied around the line. Consider the over head knot as the same knot which you would have ties to secure in place the laces of your shoes. The overhead knot can be tied simply by going over the line in order to form a loop and then going through the loop on the way back.
Tie another knot which has to be closer to the to-be-tied object. For this reason, you will have to tie the second knot further down the fishing line. When you are done, the fishing line would have two knots tied on it.
The knots need to be tightened. Accomplish this by holding both ends of the fishing line in your hand and pulling tightly. Stop pulling when you see that the knots have been tightened properly.
Get rid of the excess fishing line using a knife or a pair of scissors. If you do not have any of these tools at your disposal, simply bite on the fishing line. Although you will have to spend more effort but that is the only alternative since you do not have a cutting tool.
To finish tying the arbor knot, slowly slide second knot down the line and towards the to-be-secured object. Bring the second knot as close as possible to the object that you want to secure.