Billiards was the last PE class I would take in my undergrad program. It was a good class, and I did learn a lot in it, but I didn't have much space in my schedule from there on out for any extracurricular kind of courses.
One of the most important billiards tips I learned was how and when to use chalk. The short answer to when to use chalk is every time you hit the ball. Chalk adds friction to the tip of the cue and makes it stick to the cue ball. If you've ever lined up the perfect shot, all the angles measured perfectly, made connection with the cue ball, and had the cue fly off to one side while the cue ball flies off to the other, it's because you didn't chalk up.
With a well chalked tip, even if you don't hit perfectly in the center of the cue ball, it will grip and not skip off to the side. This is especially necessary if you want to do things like add English or spin to the ball. If you hit the cue ball just above center, the cue ball will follow the object ball. If you want the cue ball to stop as soon as it contacts the object ball, hit it at or just slightly below center. If you want it to actually roll back towards you after it hits the object ball, you hit it even further below center but not so low that you lose control of it. Doing this allows you to make sure after you've hit the object ball into the appropriate pocket, the cue ball will roll to where it should be to line up your next shot. Playing billiards can be like chess where you have to think multiple moves ahead rather than just play the shot, see where the ball lies, and then figure out your next shot. At a minimum, you can make sure the cue ball doesn't follow an object ball that's close to a pocket right down the hole by having it roll back towards you a little.
You can also add right or left English by hitting the cue ball slightly to the right or left of center. If there is an object ball frozen to the right rail (touching the bumper), you have to get that ball to spin clockwise (left English) so it rides the rail all the way to the corner pocket. To get it to spin clockwise, you would actually spin the cue ball counterclockwise (right English) by hitting the cue ball slightly to the right of center. You want the cue ball to hit the object ball on the exact opposite side from where the pocket is, and the opposite English on the cue ball will turn the object ball like a gear in the appropriate direction and hug the bumper all the way down.
In the class, we played a little bit of the standard 8-ball, which everyone seems to know how to play. Whoever gets a ball in first picks stripes or solids, get all yours in, and then go for the 8 ball. Just don't hit the 8 ball in too soon or you lose.
The big game we learned and spent most of our time on was 9-ball. It is a little different, and I think is actually my preferred game. You rack up the balls 1-9 in a diamond shape like the above picture, although the only positions that matter to the non-OCD among us are that the 1 ball is closest to you and the 9 ball is in the middle. Instead of each person hitting in a distinct set of balls, everyone is going for the same set. If you get any ball to drop, you keep playing. The basic rule is that you have to hit the lowest numbered ball first with the cue ball. If you don't or if the cue ball goes into a pocket, it's a scratch, and you've probably given away the game, since your opponent can place the cue ball wherever they like, which will probably be at an angle where they can knock the lowest numbered ball into the 9 ball, sending the 9 ball into a pocket. That's the big difference, though, is that nobody really cares about knocking in balls 1-8. You're always trying to get the 9 in. If you can hit the 1 ball into the 9 ball, pocketing the 9 ball, you've just won the game even if every other ball is still on the table. If you don't have a shot to make on the 9 ball, you just knock in the lowest numbered ball and then aim for the next lowest, trying to get into a position as soon as you can to sink the 9.
Another game we learned, which was the bane of my existence was 3-ball. In this game, you line up any 3 balls in a straight line parallel with the length of the table. The goal is simple: sink all three balls in the fewest shots possible. If you're lucky, one will go in on the break, and you will be able to drop the other two in 2 additional shots. Only one player plays the table at a time. Once they hit 6 or 8 points or whatever the maximum is that was decided upon or sinks all the balls, the next person plays a freshly racked 3 balls. A certain number of rounds is played by each player, and whoever has the lowest score wins. Like golf, it can be addicting, because while you can and do play against others, in the end you're really just competing against yourself.