The best way is to set it and forget it. Find a carbonation guilde and determine what vol level you want based on beer style, the temperature of the beer and length of your lines. Set to the recommended PSI and in 10-14 days your beer will be carbed. In three weeks or so...you'll have CO2 hydration and it will be at the peak carbonation.
If you're in a hurry try some of the quick force carb methods these guys describe above. We've all tried them. I tend to stay away from rolling and rocking kegs anymore. A high pressure like 25-30 for 24-72 hours will generally get the beer drinkably carbed but it will still be best after 3-4 weeks on gas and you have higher risk of over carbing with quick carb methods. Some people get good results pushing gas through the liquid port or using a stone. Figure out what works for you.
The worst advice you can take honestly is set it at (pick a number) psi because that works on my system...well it aint my system. It's yours and it will be different. Trust me.
Long lines will not delay or inhibit CO2 absorption. Keep them long until you get your beer carbed. The beer in the picture is no where near carbed. Once it's carbed decide if the pour is too slow for you. If it's too slow begin to shorten the line until you get the speed you like. Take off 6 inches at a time at first then less as the lines shorten. Just know that when it's too short that's when you get excessive foam. Mine are 9 feet but all systems are unique.