One really good way to train Law and Persuasion skill is to talk about the issues with Liberal Judges. If you talk about the issues with more than 6 people per day, the game will make you miss some of those appointments until the number goes down to 6. And the highest Law skill I've seen for a Liberal Judge is 10, although I've seen Hangin' Judges with a Law skill of 12. Anyway, if you talk to 6 Liberal Judges about the issues each day (choose the "B" option each day, don't have any of them actually join you), you can train your Law and Persuasion skills, and your Law skill will gradually go up until it's equal to their Law skills. If the judges aren't that good at Law and only have a Law skill of 6, for instance, your Law skill will stop going up once it gets to 6. If their Law skill is 10, it'll stop going up once it reaches 10. And your Persuasion will keep going up each day you talk to them until it maxes out.
Anyway, that's the easiest legal way to get Law and Persuasion high. Then once you've gotten it up to 9 or 10 or so, if you want to train it further, a good technique is to go to the Courthouse and talk to the juries there, do some jury tampering. If you convince them that a crime wasn't wrong, your skills go up, and you don't get charged with any crimes or get any heat or alarm anyone at the site. If you get confronted by 12 Angry Jurors, well then that's bad, you get Jury Tampering on your criminal record, you don't want that to happen, I think that also alarms the Conservatives at the site, might even give you heat, I'm not sure. Anyway if you're successful with the jury tampering you can keep doing it until your Law skill maxes out (you can only tamper with each jury once per visit, but you can visit the Courthouse as many times as you want). Each Courthouse has 2 juries nowadays, in older versions of the game it used to just be 1.
You can also study Law at the University, that's legal too, or have one Liberal in the Squad teach your other Liberals the Law skill. Both of those cost money though. Plus if you have one Liberal in your squad teach other Liberals, they can't teach to a higher skill level than what they already know.
Anyway, getting arrested and going to trial to train all of that is a waste of time, since after you are arrested you spend the rest of the month in jail at the police station, then the next month is spent in the courthouse's jail. That wastes loads of time, my method I described above works better. Plus there's no chance of getting convicted if you aren't even arrested. Jury tampering is a serious crime though, so if you want to stay out of trouble when you train your Law skill, then after the Liberal Judges have nothing left to teach you and your Law skill is at 10, take classes at the University, if you're into doing things the legal way.
Oh yeah, and you can also learn from Hangin' Judges while you interrogate them, or if you turn them and get them to join your squad instead of being Sleepers, they can teach you (but teaching requires money). If you don't want to get in trouble for kidnapping them, but your interrogation took so long that their kidnapping got reported, then once you're done learning law from the Hangin' Judges, send them on a suicide mission and make sure that they get killed by the Conservatives. Anyone who you kidnap whose disappearance gets reported in the news and is considered a missing person, I usually send them on suicide missions and make sure they die. When you send someone on a suicide mission, have them fight someone OTHER than cops, since cops might arrest them instead of killing them. Oh, and have them kill as many Conservatives as possible before they die, it's good for people on suicide missions to go out in a blaze of glory, since that not only boosts public opinion, but also you get away with the crimes since the person who committed them is dead, and the person sent on the suicide mission can't rat you out and turn Conservative themselves once they're dead. Never have your Founder or anyone you want to keep go along on a suicide mission, of course. Having your Founder die is... well... bad.