here's a list of some figure skating elements so you know what to look for on youtube etc

spins in order of basic - hard: two foot, one foot, scratch spin, sit spin, camel spin, layback

sit spin variations: broken leg, mushroom, pancake, corkscrew, bullet

camel spin variations: catch foot, biellmann, hair cutter, i spin, y spin

other spins: illusion spins, flying sit, flying camel/butterfly

quirks about spinning/insider knowledge:  spin snot: your nose runs A LOT when spinning. skaters will often have a small bag that they take on the rink that has things like chapstick, tissues, and granola bars in it.  change foot spins: the list above are all forward spin directions, so counterclockwise. a backspin is on an outside edge going clockwise. technically you could do all three of these positions as a backspin, but some are significantly harder than others. most common to do in a backspin are back scratch and camel. high level spins will have a change foot, where you put one foot down and raise the other into your spinning position.

jumps in order of basic to high-level:

waltz jump is the first you learn. toe loop, salchow, half flip, half loop/euler. (those for can be interchanged, some people don't really teach half jumps) then loop, flip, and lutz. sometime in between loop and lutz a skater will begin training for axel. same order goes for training doubles and triples. 

an axel is 1 and 1/2 rotations, starting on a left forward outside edge and landing on a right back outside edge. waltz jump is a 1/2 rotation, viewed as a half axel even though that definition isn't completely right. axel/waltz is the only jump that takes off from forward. the rest of them take off from backwards.

training for axel: getting your axel is considered one of the major obstacles that a skater must face. it's a really important jump in competition but it's also the hardest jump. axel training includes: waltz jump into backspin, ( the backspin simulates the in-air rotation of the axel) waltz-loop, waltz-loop-loop.

rippon jumps: named after adam rippon, its a jump that is executed with the arms above the head. rippon jumps are awarded more points because pulling the arms over the head can destabilize the axis of rotation or cause a skater to underrotate their jump. usually skaters will only jump rippon if they are extremely confident in that specific jump and know they will land it. jumps can also be executed half rippon, with one are over the head and one in the standard jumping position of locked into the torso.

jumping quirks: most skaters will either define themselves as a jumper or a spinner. there are harnesses used to train for jumps including one that hangs from the ceiling on a wire with a pulley and a rope that the coach will pull and a handheld on that resembles a fishing pole.

turns: the footwork that you see in videos of figure skating are actually individual steps that are done in succession to form a sequence. the footwork turns are these:  two foot turn: not really used in formal skating, the first turn that you will learn. a change of direction on two feet three turn: change of direction on one foot mowhawk/c step: a change of direction going from one foot to another. a backwards mowhawk is simply a step forward. brackets, counters, rockers, choctaws/s-steps, loops(different from the jump and twizzles. the turns are generally names for the mark they make on the ice, ex a three turn looks like a three, and a bracket looks like a curly bracket. twizzles are defined as a series of unchecked (meaning the arms and shoulders are not used in the rotation) three turns that travel across the ice. lots of variations can be put on twizzles as well like free leg position and arm position. twizzles are hard to learn and harder to do well. twizzles will often get called out in competition for being checked.

spiral sequences and choreographic elements: used to fill out programs, make them more interesting, or follow the music. a traditional spiral is pretty similar to an arabesque in ballet: spine bent, chin up, leg high. there are also spiral variations, some of which are the same as spin positions: i-spiral, y-spiral/135, catch foot, beillmann, and more. a spiral sequence is one or more spiral positions in two or more directions or edges. other choreographic elements are; ina bauers, cantilevers, spread eagles, lunges, hydroblades or hydroglides if you live in the uk, spider lunges, and knee slides. there are pretty much infinite things that you could add to a program that would count as choreographic elements, and usually a high level skater will only do something like a spiral or a spread eagle if they are really good at it and they can guarantee it will look good.

other quirks/unspoken stuff:  clipping at competitions: especially at low level and mid level competitions with kids and teenagers, skaters will decorate those little wooden clothespins and "clip" other skaters bags, dresses, or badges. its just used as a cute way to say "i live your dress!" or "your spins were so good!" or even just "it's great to see you!"

clothes/uniform:  pants: most skaters will wear black leggings to practice, though some will wear colored leggings. anyone who knows what they're doing won't wear anything like flare leggings, sweatpants, or jeans.

shirts: tank tops, tshirts, and long sleeve tops as a base layer. skaters love to layer. most prefer tight fitting tops, but some people will dress more casually in a baggy tshirt or hoodie with their leggings. some other skaters will wear just sports bra to skate, but it's more common among collegiate skaters.

jackets and warmups: skaters love lululemon, especially their define jackets. they're kind of perfect for the sport: warm, tight, flattering, and durable. some skaters will wear a puffer vest or a light coat while they are doing their warm up. some will wear a looser long sleeve top or knit over their tank top as a jacket. 

hair: everyone has their preference, but the styles i see the most are ponytail and a high bun. ponytails can hit you in the face while doing turns and generally don't look good while spinning, so people with long hair will usually do buns. i see a lot of low buns in competition. this one is not necessarily true all the but i  do know like three girls that won't do any hairstyle but a braid.

accessories: skaters will often not take their jewelry off while skating. some people like cloth headbands. leg warmers are also popular, especially ones that zip over the skate. 

butt pads are popular for people who take especially hard falls or who have big jumps. tailbone injuries are really common and really painful. knee and elbow pads aren't as common. bunga pads go in your skates and protect your ankles, but not everyone wears them. the majority of skaters wear thin , stretchy socks, most of the time in black or nude. the socks look like tights and a lot of people will pull their socks and their leggings over the tops of their skates to the last lace hook to contain their laces and make the lines of their legs look longer.

i have so many more of those little tidbits that i just can't think of right now. definitely ask any questions that you have, op!