I've already got the basics down, and I'm doing fairly good myself, if I do say so, but suplexes are super complicated for me because I can't find out what joints to use. Can anybody help me?

This org is based on aikido. Perhaps having a chat with one of their teachers will help.

when doing a suplex you need to be lower than your opponent, lift them into the air using your shoulders, you don't actually have a suplex at this moment it is just a lift. to start the suplex you extend your hips, extend the abs and while it is not necessary extending your glutes is also a good idea. if done correctly you will raise your opponent over your head and outside the ring. im not going to tell you how to do a suplex but that should get you started.
-----
Found this entry by dropkick
Link to full tutorial

Here's the best I could get, lul.

well to start, when doing a suplex your opponent often puts himself in a position that makes it easier for you to suplex. Also you want to utilize your wrists, Say you are in a grapple war with your opponent, you want to have your wrists contracted when lifting and then extend mid lift to help flip your opponent over your body and outside the wring, also play with your chest and lumbar as they often make suplexing much easier.

Here are 2 suplexes of me in game maybe they help maybe they dont,
-----
Btw its easier while playing against actuall players, they can give you momentum and it can learn you to adapt your suplex like shown in the first replay.
My opinion

And plus don't try and suplex to early or you will ending just lifting them forward. Wait till you are leaning back some and work with your ankles.

Another joint that's really important is that you want to extend abs to get some weight backwards

Suplex can be tricky as it uses your opponent's momentum most of the time.
In general you'll want to do what others explained, grab your opponent's legs or hips then lift him.
But there are many ways it can end up.
If your opponent is smart enough or if you do it too soon, he will not give you what you need to throw him behind you but you can manage that by either slaming him in front of you (out of ring) (by jumping forward then contracting both hips when they can touche the ground) or on the side (by playing with your pecs and torso and gluts)

The most effective way, in my opinion, to throw a suplex is by grabbing your opponent by the leg with one hand and an upper body part with the other. This can give you complete control over the way you'll lift him, as you will be able to control both his upper and lower body direction more easily, and slam his face to the ground in any direction you want.

You can try some openings to start the suplexes in free mod, but you'll find it very difficult to do, it's way easier with a moving target, ironically.