When I used to do Aikido, we sometimes land in awkward positions, so we would always stretch for a side spit before each class. I've always wanted to kick higher too, so I just did the stretches every night before bed. I think I was able to achieve a side split within a few months of regular stretching. To "train" for the splits, I would sit on the floor and spread my legs as far apart as possible. Then I take them in a couple inches. I would then lean forward with a straight back to feel the stretch in my inner thighs and knees. Go as far down as you can, I usually aim to put my chin on my hands and have my elbows touch the floor (straight back! no rounding). As you get more flexible, you can actually reach forward and nearly put your entire torso on the floor. I'd do this stretch everyday (among others) and aim for just a bit more of a split each time. Always back out of the spread position by sitting back up, putting your hands behind you and pulling/dragging your butt backwards so your legs close up a bit.
The front splits were harder. I had to start stretching for these when I did a quick stint in kung fu, and I never enjoyed stretching for those. There was no alternative stretching position, so "training" was just trying to do the splits and holding for a minute. I was able to do some okay front splits after several months of stretching. I find it's the hip flexors that were always tough rather then the hamstrings.
There's a couple schools of thought on stretching, but I went with cold static stretching with very controlled bouncing where applicable. I know it's not recommended due to high rate of injury for the less careful, but it was recommended to me by my instructor and it worked out for me.
I'll probably make a Hub one day with the "program" of stretches I would do for my lower body. It targeted most areas including hamstrings, quads, inner thighs, and even the IT band. Hard to describe by words, so may even have to do pictures.