You can only begin training with Freiza if you see him wandering around TokiToki city after completing your training with Ginyu. You must also be level 20 or higher, though leveling a bit more will make the lessons that much easier.
The first test is like any other. You simply whittle down Frieza's health until he concedes and accepts you as a student. This will grant you the skill "Death Beam". Now that he has accepted you as his student, you will see that he stands before you after each mission in front of the statue.
If you haven't already, press
and equip your new skill. It's not necessary you have to use it, like they say, however it does help to have it on. You'll then wish to start completing Parallel Quests in order to boost the bond. You'll want to pick "Freiza 1st Form". It's been disputed that the others do or don't work, I found it went slower if I picked the others which leads me to believe it doesn't. It doesn't make much difference anyway, so you may as well play it safe and choose the first. Play these quests and speak to Freiza each time for a chance of an item and a boost to your bond. You'll know you've unlocked another training session when he has a blue question mark above his head.
Training 2 gives you Death Crasher, a Strike ability. As you did before, equip this one and resume questing. He'll also ask you for an All-Regen Shard. You can find these laying about on the ground in the lower, level PQ's. These are marked with a red question mark and you can find them with your scouter (Left on the D-Pad during battle). After giving him the item, resume your training as you had before.
Training 3 gives you Emperor's Sign. This skill offers varying effects by race. I didn't find it particularly useful, but I still equipped it for the sake of boosting the bond gained. Repeat the process once more until the bar has filled and you see Freiza is ready to offer you the final lesson. You will face him in combat in his first form. Once you lower his health to half, he'll transform in to his Final Form with a new health bar. Deplete this to approximately 10% and you'll complete the training and be awarded your achievement, the ultimate attack "Supernova" and one of his Z-Skills.
As with any training, once this has concluded you can find a new master and replace the skills you had equipped. If you wish to stop mid-training and find a new master, you'll keep the bond you had already gained. If you wish to hasten the process, PQ 43 is a good option as Magnificent X has posted. Personally, I'd suggest just working towards this while trying to get the various skills you'll have to obtain for the 100% however the decision is yours to make.