I wrap the end of the line with masking tape and then cut thru the masking tape and line with a sharp utility knife. Then I carefully heat the end hot enough to melt is, usually with a lighter or propane torch. Try not to set it on fire. Take the tape off and inspect to see if the mantle (outside covering) has melted enough to keep it from fraying. If not, just heat it until it does. You can put electrical tape around the end of the line if you like, but it only lasts a season or so before it needs to be replaced.
Fusing the ends is definitely the easiest method. However, I cheated. I brought a spool of line and a list of the required lengths to our Boy Scout meeting and let the boys practice doing whippings for a real life situation. Haven't had any come apart yet so I guess we taught them well.