What is the most popular way to fix constipation problems?

Fiber and fluids. Simple constipation usually responds to a diet rich in fiber (bran, whole grain cereals, fruits, vegetables) and increased fluid intake (water is sufficient). Several significant causes of constipation other than bad diet should be investigated with the help of your doctor e.g. Hypothroidism, hirschprung's disease among others.
Popular is not best. Fad treatment approaches come & go--dating to "snake oil" salesmen of yesteryear. Colonics & purges are popular but should be avoided & can not be recommended (see earlier healthtap answers). Use of irritant laxatives are safe for the short-term only. Fiber supplements, stool softeners, & lavage agents like MiraLAX (polyethylene glycol) are safe. Rx drugs are available, based on work-up of your cause of constipation.
Diet, fluids. Foods high in fat tend to constipate you. Foods high in fiber favor looser stools. Fruits vegetable, whole grains are excellent sources of fiber. Also, fiber only works if u are well hydrated. Drink plenty of non-caffinated, non-alcoholic fluids to keep stools soft. Fiber can also be added to a glass of water. If this does not work see a GI specialist, there may be another cause of your issu.