I am 21 years of age. I have been learning taekwondo for a year. However, I am still unable to achieve a complete split. What are exercises that I can do to increase my flexibility to reach a complete split?
I agree with Robin that squats and deadlifts are important. but i disagree that if you can't squat your own body weight you shouldn't be doing martial arts.
Squats are actually great for improving your hip flexibility, most people think they are only for strengthening, but they definitely improve your hip and ankle flexibility. Just make sure your form is good or you'll do more damage then good!
My favourite way to improve flexibility, which I have talked about in a few questions here, is active stretching, or stretching with a partner also known in more science like terms as isometric stretching. Here's a link to an answer to another questions: Is stretching with a partner beneficial, dangerous, or both?
For doing the splits, I would work on the one standing against the wall primarily. Doing the butterfly stretch won't hurt either.
To do the first one:
Make sure you do both sides b/c the stretch is difference depending which leg is in the air!
Also: Make sure you're very warm before doing any flexibility work. working on flexibility cold is not very helpful, and can be quite harmful.
Deadlifts and squats. Thomas Kurz (who demonstrates some very impressive splits at a moderately old age) says that if you can't deadlift and squat your own bodyweight (minimum), you really shouldn't be training for martial arts or flexibility.