Static Stretching. 
One of the most simple and effective ways to improve flexibility is to do some static stretches. A basic example of this is bending over and touching your toes to stretch, this stretches the hamstring muscles in the back of the legs as well as the upper and lower back muscles. Stretches should be held for around 30-60 seconds and repeated 3 times.

Variety is key. 
Performing a larger variety of stretches for each muscle group is beneficial for increasing flexibility. This will ensure the muscles are hit from different angles and will help prevent any imbalances. It is also important that when doing intense stretching sessions to change the muscles targeted each day, just like you would if you were weight training. 

Stretch linked muscle groups. 
When focused on increasing the flexibility of a certain muscle group, stretching other inter-connected muscles will help. For example when wanting to improve hamstring flexibility, it is recommended that the lower back, buttocks and calves are also stretched. These muscle groups are all linked and this is why when a person has tight hamstrings it can lead to pains in other muscles such as those in the lower back.

Stretch when muscles are warm. 
Stretching should only be done when the muscles are warm such as after a workout as this is when the muscles are most pliable. If you want to do a light stretching session multiple times a day however then doing a short 5 minute warm up prior to stretching is recommended. There are two main reasons for this, firstly and most importantly it will reduce the risk of injuring the muscle. Secondly because the muscle is more pliable it will allow the target muscles to be stretched further therefore allowing the most benefits to be gained from the stretch.

Combine stretching a foam rolling. 
Self massage using foam rollers is extremely popular at the moment especially among professional athletes. It is thought that it helps loosen up the muscles and break down any scar tissue. This then helps improve flexibility and increase Range of Motion (ROM). One study found that a combination of foam rolling and static stretching resulted in greater improvements in flexibility than either foam rolling or static stretching alone [1]

References:

[1]https://www.researchgate.net/profile/Blaine_Long/publication/259883124_Foam_Rolling_and_Static_Stretching_on_Passive_Hip_Flexion_Range_of_Motio